CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT171+7 : TPTP v9.2.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:06:21 PM UTC 2026

% Result   : Theorem 2.74s 2.94s
% Output   : CNFRefutation 2.86s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1517)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_45__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_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(fact_47_notin__Lin__iff,axiom,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X7),X6)),X8)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_notin__Lin__iff) ).

fof(fact_512_imageE,axiom,
    ! [X1,X2,X15,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
     => ~ ! [X26] :
            ( ti(X1,X15) = hAPP(X2,X1,X38,X26)
           => ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_imageE) ).

fof(fact_124_linorder__antisym__conv2,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_linorder__antisym__conv2) ).

fof(fact_70_linorder__antisym__conv3,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_linorder__antisym__conv3) ).

fof(fact_119_linorder__antisym__conv1,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_linorder__antisym__conv1) ).

fof(fact_164_linorder__neqE__linordered__idom,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X34,X35] :
          ( ti(X1,X34) != ti(X1,X35)
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_linorder__neqE__linordered__idom) ).

fof(fact_72_not__less__iff__gr__or__eq,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
            | ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_not__less__iff__gr__or__eq) ).

fof(fact_69_linorder__neqE,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ti(X1,X34) != ti(X1,X35)
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_linorder__neqE) ).

fof(fact_53_linorder__cases,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ( ti(X1,X34) != ti(X1,X35)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_linorder__cases) ).

fof(fact_202_equalityE,axiom,
    ! [X1,X40,X43] :
      ( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
         => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_equalityE) ).

fof(help_fequal_1_1_T,axiom,
    ! [X1,X34,X35] :
      ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35))
      | ti(X1,X34) = ti(X1,X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

fof(fact_757_folding__image_Oeq__general__inverses,axiom,
    ! [X2,X1,X39,X63,X76,X57,X103,X41,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
       => ( ! [X46] :
              ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
             => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X57,X46)),X41))
                & hAPP(X2,X2,X76,hAPP(X2,X2,X57,X46)) = ti(X2,X46) ) )
         => ( ! [X26] :
                ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
               => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X2,X2,X76,X26)),X103))
                  & hAPP(X2,X2,X57,hAPP(X2,X2,X76,X26)) = ti(X2,X26)
                  & hAPP(X2,X1,X39,hAPP(X2,X2,X76,X26)) = hAPP(X2,X1,X63,X26) ) )
           => hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X63),X41) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X103) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_folding__image_Oeq__general__inverses) ).

fof(help_COMBI_1_1_U,axiom,
    ! [X1,X118] : hAPP(X1,X1,combi(X1),X118) = ti(X1,X118),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).

fof(fact_710_fold__image__eq__general__inverses,axiom,
    ! [X2,X1,X3] :
      ( comm_monoid_mult(X3)
     => ! [X99,X39,X38,X76,X57,X103,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ! [X46] :
                ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),X103))
               => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X57,X46)),X41))
                  & hAPP(X1,X2,X76,hAPP(X2,X1,X57,X46)) = ti(X2,X46) ) )
           => ( ! [X26] :
                  ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
                 => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X76,X26)),X103))
                    & hAPP(X2,X1,X57,hAPP(X1,X2,X76,X26)) = ti(X1,X26)
                    & hAPP(X2,X3,X39,hAPP(X1,X2,X76,X26)) = hAPP(X1,X3,X38,X26) ) )
             => hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X38),X99),X41) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X99),X103) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_fold__image__eq__general__inverses) ).

fof(fact_94__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_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
       => ( ! [X33] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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/sandbox/benchmark/theBenchmark.p',fact_94__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O) ).

fof(fact_521_pigeonhole__infinite,axiom,
    ! [X2,X1,X38,X40] :
      ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( 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),X38),X40)))
       => ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
            & ~ 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),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)),X40))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X38)),hAPP(X1,X2,X38,X26)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_pigeonhole__infinite) ).

fof(fact_428_card__less__Suc2,axiom,
    ! [X29,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)),X29)))) = 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,X29))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_card__less__Suc2) ).

fof(fact_988_setsum__delta,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X15,X14,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
            & ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_setsum__delta) ).

fof(fact_987_setsum__delta_H,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X15,X14,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
            & ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_setsum__delta_H) ).

fof(fact_6__C2_C,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
       => ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
         => ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C) ).

fof(fact_7__C1_C,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
       => ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X13)
         => ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
                   => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C) ).

fof(fact_9_pairwise__neutrality,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( ti(arrow_2142409994le_alt,X12) != ti(arrow_2142409994le_alt,X13)
       => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
         => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
           => ( ! [X16] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
             => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X12),X13)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

fof(fact_84__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_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84__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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

fof(fact_8__C4_C,axiom,
    ! [X10,X11,X17,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( ti(arrow_2142409994le_alt,X15) != ti(arrow_2142409994le_alt,X17)
       => ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X17)
         => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
           => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
             => ( ! [X16] :
                    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
               => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X17)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C) ).

fof(fact_81_dictatorI,axiom,
    ! [X29,X25] :
      ( hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X25),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin))))
     => ( ! [X26] :
            ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
           => ! [X19,X20] :
                ( ti(arrow_2142409994le_alt,X19) != ti(arrow_2142409994le_alt,X20)
               => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29)))
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) )
       => hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dictatorI) ).

fof(fact_10__C3_C,axiom,
    ! [X10,X11,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X11),arrow_301600364e_Prof))
       => ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X10),arrow_301600364e_Prof))
         => ( ! [X16] :
                ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X11,X16)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X10,X16))) )
           => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X11)))
            <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X10))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C) ).

fof(fact_91_in__below,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X14),X15)))
        <=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
            & ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X14)
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X15)),X8)) )
            & ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X14)
             => ( ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
                 => ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
                    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X7)),X8)) ) )
                & ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X14)
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_in__below) ).

fof(fact_79_in__above,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X14),X15)))
        <=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
            & ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X15)
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X7)),X8)) )
            & ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X15)
             => ( ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X15)
                 => ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X14)
                    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X14)),X8)) ) )
                & ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X15)
                 => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_in__above) ).

fof(fact_686_sum__squares__le__zero__iff,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))),zero_zero(X1)))
        <=> ( ti(X1,X6) = zero_zero(X1)
            & ti(X1,X7) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_sum__squares__le__zero__iff) ).

fof(fact_688_not__sum__squares__lt__zero,axiom,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X34,X35] : ~ 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),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35))),zero_zero(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_not__sum__squares__lt__zero) ).

fof(fact_80_pred__equals__eq2,axiom,
    ! [X1,X2,X41,X42] :
      ( ! [X26,X27] :
          ( 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),X26),X27)),X42))
        <=> 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),X26),X27)),X41)) )
    <=> ti(fun(product_prod(X1,X2),bool),X42) = ti(fun(product_prod(X1,X2),bool),X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pred__equals__eq2) ).

fof(fact_546_inv__into__funcset,axiom,
    ! [X2,X1,X38,X40,X43] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)),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),X43),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X40)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_inv__into__funcset) ).

fof(fact_713_image__cong,axiom,
    ! [X2,X1,X38,X39,X71,X60] :
      ( ti(fun(X1,bool),X71) = ti(fun(X1,bool),X60)
     => ( ! [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X60))
           => hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
       => hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X71) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X39),X60) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_image__cong) ).

fof(fact_307_folding__image__simple__idem_Oidem,axiom,
    ! [X2,X1,X6,X38,X9,X39,X25] :
      ( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
     => hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X6),X6) = ti(X1,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_folding__image__simple__idem_Oidem) ).

fof(fact_140_below__Lin,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_below__Lin) ).

fof(fact_51_above__Lin,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X8),X6),X7)),arrow_1568854078le_Lin)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_above__Lin) ).

fof(fact_501_pigeonhole,axiom,
    ! [X1,X2,X38,X40] :
      ( 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),X38),X40))),hAPP(fun(X2,bool),nat,finite_card(X2),X40)))
     => ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_pigeonhole) ).

fof(fact_687_sum__squares__gt__zero__iff,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X6,X7] :
          ( 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7))))
        <=> ( ti(X1,X6) != zero_zero(X1)
            | ti(X1,X7) != zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_sum__squares__gt__zero__iff) ).

fof(fact_48_Lin__irrefl,axiom,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),X8)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Lin__irrefl) ).

fof(fact_569_Id__compose,axiom,
    ! [X1,X2,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
       => hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X40),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X43)),X38) = ti(fun(X1,X2),X38) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_Id__compose) ).

fof(fact_4_in__mkbot,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X9)))
    <=> ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
        & ( ti(arrow_2142409994le_alt,X6) = ti(arrow_2142409994le_alt,X9)
         => ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
        & ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

fof(fact_5_in__mktop,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X9)))
    <=> ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X9)
        & ( ti(arrow_2142409994le_alt,X7) = ti(arrow_2142409994le_alt,X9)
         => ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7) )
        & ( ti(arrow_2142409994le_alt,X7) != ti(arrow_2142409994le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop) ).

fof(fact_568_compose__Id,axiom,
    ! [X1,X2,X39,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
       => hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X40),X39),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X40)) = ti(fun(X1,X2),X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_compose__Id) ).

fof(fact_856_sup2E,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_sup2E) ).

fof(fact_972_inf2E,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => ~ ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
         => ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_inf2E) ).

fof(fact_476_inv__into__injective,axiom,
    ! [X2,X1,X40,X38,X6,X7] :
      ( 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),X40),X38),X6) = 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),X40),X38),X7)
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
         => ti(X2,X6) = ti(X2,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_inv__into__injective) ).

fof(fact_769_atLeastatMost__psubset__iff,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X14,X15,X17,X81] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
              | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
                & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81))
                & ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X14))
                  | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) )
            & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X81)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_atLeastatMost__psubset__iff) ).

fof(fact_711_extensionalityI,axiom,
    ! [X1,X2,X39,X38,X40] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
     => ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
       => ( ! [X26] :
              ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
             => hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
         => ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_extensionalityI) ).

fof(fact_762_atLeastatMost__subset__iff,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_atLeastatMost__subset__iff) ).

fof(fact_494_endo__inj__surj,axiom,
    ! [X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( 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),X38),X40)),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
         => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40) = ti(fun(X1,bool),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_endo__inj__surj) ).

fof(fact_87_PiE,axiom,
    ! [X1,X2,X6,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
     => ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_PiE) ).

fof(fact_564_surj__compose,axiom,
    ! [X3,X2,X1,X39,X52,X38,X40,X43] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
     => ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),X43) = ti(fun(X3,bool),X52)
       => 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)),hAPP(fun(X2,bool),fun(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3))),compose(X2,X1,X3),X40),X39),X38)),X40) = ti(fun(X3,bool),X52) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_surj__compose) ).

fof(fact_965_setsum__cl__ivl__Suc,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X30,X54] :
          ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
          & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X30))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_setsum__cl__ivl__Suc) ).

fof(fact_736_o__inv__o__cancel,axiom,
    ! [X3,X1,X2,X39,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),X39),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))),X38))),X38) = ti(fun(X1,X3),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_o__inv__o__cancel) ).

fof(fact_857_sup2CI,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) )
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_sup2CI) ).

fof(fact_562_compose__id__inv__into,axiom,
    ! [X2,X1,X38,X40,X43] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X43)
     => hAPP(fun(X1,X2),fun(X1,X1),hAPP(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1)),hAPP(fun(X1,bool),fun(fun(X2,X1),fun(fun(X1,X2),fun(X1,X1))),compose(X1,X2,X1),X43),X38),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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),X40),X38)),X43)) = hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X43) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_compose__id__inv__into) ).

fof(fact_577_crossproduct__eq,axiom,
    ! [X1] :
      ( semiri456707255roduct(X1)
     => ! [X91,X7,X6,X9] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X9)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X91),X9)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X7))
        <=> ( ti(X1,X91) = ti(X1,X6)
            | ti(X1,X7) = ti(X1,X9) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_crossproduct__eq) ).

fof(fact_580_crossproduct__noteq,axiom,
    ! [X1] :
      ( semiri456707255roduct(X1)
     => ! [X17,X81,X14,X15] :
          ( ( ti(X1,X14) != ti(X1,X15)
            & ti(X1,X17) != ti(X1,X81) )
        <=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X81)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X81)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_crossproduct__noteq) ).

fof(fact_558_f__the__inv__into__f,axiom,
    ! [X1,X2,X7,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
       => hAPP(X1,X2,X38,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7)) = ti(X2,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_f__the__inv__into__f) ).

fof(fact_484_image__inv__into__cancel,axiom,
    ! [X2,X1,X82,X38,X40,X48] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40) = ti(fun(X1,bool),X48)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X82),X48))
       => hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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),X40),X38)),X82)) = ti(fun(X1,bool),X82) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_image__inv__into__cancel) ).

fof(fact_964_setsum__op__ivl__Suc,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X30,X54] :
          ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
          & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(nat,X1,X38,X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_setsum__op__ivl__Suc) ).

fof(fact_485_image__surj__f__inv__f,axiom,
    ! [X2,X1,X40,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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),top_top(fun(X2,bool))),X38)),X40)) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_image__surj__f__inv__f) ).

fof(fact_474_f__inv__into__f,axiom,
    ! [X1,X2,X7,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
     => hAPP(X2,X1,X38,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),X40),X38),X7)) = ti(X1,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_f__inv__into__f) ).

fof(fact_480_range__ex1__eq,axiom,
    ! [X1,X2,X15,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),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)))))
      <=> ? [X26] :
            ( ti(X2,X15) = hAPP(X1,X2,X38,X26)
            & ! [X46] :
                ( ti(X2,X15) = hAPP(X1,X2,X38,X46)
               => ti(X1,X46) = ti(X1,X26) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_range__ex1__eq) ).

fof(fact_514_finite__subset__image,axiom,
    ! [X2,X1,X38,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
       => ? [X85] :
            ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X85),X40))
            & hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X85))
            & ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X85) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_finite__subset__image) ).

fof(fact_275_inj__on__inverseI,axiom,
    ! [X2,X1,X39,X38,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_inj__on__inverseI) ).

fof(fact_502_inv__into__image__cancel,axiom,
    ! [X1,X2,X41,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X41),X40))
       => 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),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X41)) = ti(fun(X1,bool),X41) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_inv__into__image__cancel) ).

fof(fact_780_inj__on__Un__image__eq__iff,axiom,
    ! [X1,X2,X38,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
     => ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
      <=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_inj__on__Un__image__eq__iff) ).

fof(fact_463_subset__image__iff,axiom,
    ! [X1,X2,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
    <=> ? [X79] :
          ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X79),X40))
          & ti(fun(X1,bool),X43) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X79) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_subset__image__iff) ).

fof(fact_849_le__supE,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X22,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34))
         => ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
             => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_le__supE) ).

fof(fact_774_UnE,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_UnE) ).

fof(fact_193_add__leE,axiom,
    ! [X49,X50,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_add__leE) ).

fof(fact_468_image__iff,axiom,
    ! [X1,X2,X9,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X9),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
          & ti(X1,X9) = hAPP(X2,X1,X38,X26) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__iff) ).

fof(fact_636_not__square__less__zero,axiom,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21)),zero_zero(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_not__square__less__zero) ).

fof(fact_281_card__seteq,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X43)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
         => ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_card__seteq) ).

fof(fact_233_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/sandbox/benchmark/theBenchmark.p',fact_233_not__add__less1) ).

fof(fact_234_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/sandbox/benchmark/theBenchmark.p',fact_234_not__add__less2) ).

fof(fact_869_IntE,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
     => ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
         => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_IntE) ).

fof(fact_506_image__inv__f__f,axiom,
    ! [X1,X2,X40,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_image__inv__f__f) ).

fof(fact_505_inv__image__comp,axiom,
    ! [X1,X2,X83,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => 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))),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X83)) = ti(fun(X1,bool),X83) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_inv__image__comp) ).

fof(fact_455_card__def,axiom,
    ! [X1,X40] :
      ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) )
      & ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_card__def) ).

fof(fact_557_the__inv__into__onto,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => 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)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_the__inv__into__onto) ).

fof(fact_522_finite__conv__nat__seg__image,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
    <=> ? [X44,X84] : ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_finite__conv__nat__seg__image) ).

fof(fact_516_nat__seg__image__imp__finite,axiom,
    ! [X1,X40,X38,X30] :
      ( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X38),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)),X30)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_nat__seg__image__imp__finite) ).

fof(fact_520_rangeE,axiom,
    ! [X1,X2,X15,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool)))))
     => ~ ! [X26] : ti(X1,X15) != hAPP(X2,X1,X38,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_rangeE) ).

fof(fact_487_surj__iff__all,axiom,
    ! [X2,X1,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
    <=> ! [X26] : hAPP(X2,X1,X38,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),top_top(fun(X2,bool))),X38),X26)) = ti(X1,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_surj__iff__all) ).

fof(fact_970_setsum_OF__eq,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X40] :
          ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
           => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) )
          & ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
           => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_setsum_OF__eq) ).

fof(fact_88_complete__Lin,axiom,
    ! [X14,X15] :
      ( ti(arrow_2142409994le_alt,X14) != ti(arrow_2142409994le_alt,X15)
     => ? [X26] :
          ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X26),arrow_1568854078le_Lin))
          & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_complete__Lin) ).

fof(fact_137_inj__on__iff,axiom,
    ! [X1,X2,X7,X6,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
         => ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
          <=> ti(X1,X6) = ti(X1,X7) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_inj__on__iff) ).

fof(fact_138_inj__onD,axiom,
    ! [X1,X2,X6,X7,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
           => ti(X1,X6) = ti(X1,X7) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_inj__onD) ).

fof(fact_136_inj__on__contraD,axiom,
    ! [X1,X2,X6,X7,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( ti(X1,X6) != ti(X1,X7)
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),X40))
           => hAPP(X1,X2,X38,X6) != hAPP(X1,X2,X38,X7) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_inj__on__contraD) ).

fof(fact_135_inj__on__def,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => ! [X27] :
              ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
             => ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X27)
               => ti(X1,X26) = ti(X1,X27) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_inj__on__def) ).

fof(fact_458_image__eqI,axiom,
    ! [X1,X2,X40,X15,X38,X6] :
      ( ti(X1,X15) = hAPP(X2,X1,X38,X6)
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_image__eqI) ).

fof(fact_470_rev__image__eqI,axiom,
    ! [X2,X1,X15,X38,X6,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
     => ( ti(X2,X15) = hAPP(X1,X2,X38,X6)
       => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X15),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_rev__image__eqI) ).

fof(fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [X32] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),X32))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X32),arrow_1568854078le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X31),arrow_1568854078le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(fact_148_inv__into__f__eq,axiom,
    ! [X1,X2,X7,X6,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
         => 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),X40),X38),X7) = ti(X1,X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_inv__into__f__eq) ).

fof(fact_552_the__inv__into__f__eq,axiom,
    ! [X1,X2,X6,X7,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
         => hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X7) = ti(X1,X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_the__inv__into__f__eq) ).

fof(fact_777_UnCI,axiom,
    ! [X1,X40,X17,X43] :
      ( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_UnCI) ).

fof(fact_147_inv__into__f__f,axiom,
    ! [X1,X2,X6,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => 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),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_inv__into__f__f) ).

fof(fact_553_the__inv__into__f__f,axiom,
    ! [X1,X2,X6,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_the__inv__into__f__f) ).

fof(fact_920_le__infE,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)))
         => ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
             => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_le__infE) ).

fof(fact_654_add__scale__eq__noteq,axiom,
    ! [X1] :
      ( semiri456707255roduct(X1)
     => ! [X37,X45,X21,X22,X97] :
          ( ti(X1,X97) != zero_zero(X1)
         => ( ( ti(X1,X21) = ti(X1,X22)
              & ti(X1,X37) != ti(X1,X45) )
           => hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X37)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X97),X45)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_add__scale__eq__noteq) ).

fof(fact_775_sup1E,axiom,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6))
     => ( ~ hBOOL(hAPP(X1,bool,X40,X6))
       => hBOOL(hAPP(X1,bool,X43,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_sup1E) ).

fof(fact_653_sum__squares__eq__zero__iff,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X6,X7] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X7),X7)) = zero_zero(X1)
        <=> ( ti(X1,X6) = zero_zero(X1)
            & ti(X1,X7) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_sum__squares__eq__zero__iff) ).

fof(fact_150_inj__imp__inv__eq,axiom,
    ! [X1,X2,X39,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( ! [X26] : hAPP(X1,X2,X38,hAPP(X2,X1,X39,X26)) = ti(X2,X26)
       => 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))),X38) = ti(fun(X2,X1),X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_inj__imp__inv__eq) ).

fof(tsy_c_Finite__Set_Ofolding__image_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image_res) ).

fof(fact_868_inf1E,axiom,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
     => ~ ( hBOOL(hAPP(X1,bool,X40,X6))
         => ~ hBOOL(hAPP(X1,bool,X43,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_inf1E) ).

fof(fact_473_atLeastLessThan__eq__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X17,X81,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
           => ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
            <=> ( ti(X1,X14) = ti(X1,X17)
                & ti(X1,X15) = ti(X1,X81) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_atLeastLessThan__eq__iff) ).

fof(fact_472_atLeastLessThan__inj_I1_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
             => ti(X1,X14) = ti(X1,X17) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_atLeastLessThan__inj_I1_J) ).

fof(fact_471_atLeastLessThan__inj_I2_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X14),X15) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X81))
             => ti(X1,X15) = ti(X1,X81) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_atLeastLessThan__inj_I2_J) ).

fof(fact_671_extensional__restrict,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
     => hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = ti(fun(X1,X2),X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_extensional__restrict) ).

fof(fact_405_not__less__eq__eq,axiom,
    ! [X54,X30] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_not__less__eq__eq) ).

fof(fact_486_surj__f__inv__f,axiom,
    ! [X2,X1,X7,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => hAPP(X2,X1,X38,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),top_top(fun(X2,bool))),X38),X7)) = ti(X1,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_surj__f__inv__f) ).

fof(fact_523_finite__imp__nat__seg__image__inj__on,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ? [X44,X84] :
          ( ti(fun(X1,bool),X40) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X84),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)),X44)))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),X84),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)),X44)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_finite__imp__nat__seg__image__inj__on) ).

fof(tsy_c_Finite__Set_Ofolding__image__simple__idem_res,axiom,
    ! [X1,X2] : 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),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).

fof(fact_159_less__fun__def,axiom,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X38,X39] :
          ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X38),X39))
        <=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
            & ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X39),X38)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_less__fun__def) ).

fof(fact_482_inj__image__eq__iff,axiom,
    ! [X1,X2,X40,X43,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)
      <=> ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_inj__image__eq__iff) ).

fof(fact_513_surj__imp__inv__eq,axiom,
    ! [X2,X1,X39,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => ( ! [X26] : hAPP(X1,X2,X39,hAPP(X2,X1,X38,X26)) = ti(X2,X26)
       => hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X38) = ti(fun(X1,X2),X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_surj__imp__inv__eq) ).

fof(fact_992_setsum__eq__Suc0__iff,axiom,
    ! [X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = hAPP(nat,nat,suc,zero_zero(nat))
      <=> ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
            & hAPP(X1,nat,X38,X26) = hAPP(nat,nat,suc,zero_zero(nat))
            & ! [X27] :
                ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
               => ( ti(X1,X26) != ti(X1,X27)
                 => hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_setsum__eq__Suc0__iff) ).

fof(fact_465_range__eqI,axiom,
    ! [X1,X2,X15,X38,X6] :
      ( ti(X1,X15) = hAPP(X2,X1,X38,X6)
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_range__eqI) ).

fof(fact_212_set__eq__subset,axiom,
    ! [X1,X40,X43] :
      ( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
        & hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_set__eq__subset) ).

fof(fact_194_equalityI,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
       => ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_equalityI) ).

fof(fact_85_inv__f__eq,axiom,
    ! [X1,X2,X6,X7,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hAPP(X1,X2,X38,X6) = ti(X2,X7)
       => 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))),X38),X7) = ti(X1,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_inv__f__eq) ).

fof(fact_86_inv__f__f,axiom,
    ! [X1,X2,X6,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => 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))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_inv__f__f) ).

fof(fact_555_the__inv__f__f,axiom,
    ! [X1,X2,X6,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),top_top(fun(X1,bool))),X38),hAPP(X1,X2,X38,X6)) = ti(X1,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_the__inv__f__f) ).

fof(fact_343_add__nonneg__eq__0__iff,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X7))
           => ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X6),X7) = zero_zero(X1)
            <=> ( ti(X1,X6) = zero_zero(X1)
                & ti(X1,X7) = zero_zero(X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_add__nonneg__eq__0__iff) ).

fof(fact_993_setsum__eq__1__iff,axiom,
    ! [X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X40) = one_one(nat)
      <=> ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
            & hAPP(X1,nat,X38,X26) = one_one(nat)
            & ! [X27] :
                ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
               => ( ti(X1,X26) != ti(X1,X27)
                 => hAPP(X1,nat,X38,X27) = zero_zero(nat) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_setsum__eq__1__iff) ).

fof(fact_396_not__less__eq,axiom,
    ! [X54,X30] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_not__less__eq) ).

fof(fact_197_subset__iff__psubset__eq,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
        | ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_subset__iff__psubset__eq) ).

fof(fact_196_psubset__eq,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
        & ti(fun(X1,bool),X40) != ti(fun(X1,bool),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_psubset__eq) ).

fof(fact_776_sup1CI,axiom,
    ! [X1,X40,X43,X6] :
      ( ( ~ hBOOL(hAPP(X1,bool,X43,X6))
       => hBOOL(hAPP(X1,bool,X40,X6)) )
     => hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_sup1CI) ).

fof(fact_401_le__SucE,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
       => X49 = hAPP(nat,nat,suc,X51) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_le__SucE) ).

fof(fact_115_less__le__not__le,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
            & ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_less__le__not__le) ).

fof(fact_393_not__less__less__Suc__eq,axiom,
    ! [X30,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
      <=> X30 = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_not__less__less__Suc__eq) ).

fof(fact_392_less__antisym,axiom,
    ! [X51,X49] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X49)))
       => X49 = X51 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_less__antisym) ).

fof(fact_388_less__SucE,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
       => X49 = X51 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_less__SucE) ).

fof(fact_108_order__eq__iff,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X6,X7] :
          ( ti(X1,X6) = ti(X1,X7)
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
            & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__eq__iff) ).

fof(fact_105_order__antisym__conv,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_order__antisym__conv) ).

fof(fact_100_order__antisym,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
           => ti(X1,X34) = ti(X1,X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order__antisym) ).

fof(fact_98_xt1_I5_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
           => ti(X1,X34) = ti(X1,X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_xt1_I5_J) ).

fof(fact_733_K__record__comp,axiom,
    ! [X1,X2,X3,X17,X38,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X17)),X38),X26) = ti(X2,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_K__record__comp) ).

fof(fact_406_Suc__n__not__le__n,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_Suc__n__not__le__n) ).

fof(fact_367_ex__least__nat__less,axiom,
    ! [X30,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X30))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X30))
            & ! [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/sandbox/benchmark/theBenchmark.p',fact_367_ex__least__nat__less) ).

fof(fact_528_surjI,axiom,
    ! [X2,X1,X39,X38] :
      ( ! [X26] : hAPP(X2,X1,X39,hAPP(X1,X2,X38,X26)) = ti(X1,X26)
     => hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_surjI) ).

fof(fact_67_order__less__not__sym,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order__less__not__sym) ).

fof(fact_66_order__less__imp__not__less,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_order__less__imp__not__less) ).

fof(fact_62_order__less__asym_H,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_order__less__asym_H) ).

fof(fact_54_order__less__asym,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_order__less__asym) ).

fof(fact_112_linorder__not__le,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_linorder__not__le) ).

fof(fact_122_leD,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_leD) ).

fof(fact_111_linorder__not__less,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_linorder__not__less) ).

fof(fact_61_xt1_I9_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_xt1_I9_J) ).

fof(fact_103_xt1_I3_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X37,X21,X22] :
          ( ti(X1,X21) = ti(X1,X22)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_xt1_I3_J) ).

fof(fact_101_xt1_I4_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
         => ( ti(X1,X22) = ti(X1,X37)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_xt1_I4_J) ).

fof(fact_59_xt1_I1_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X37,X21,X22] :
          ( ti(X1,X21) = ti(X1,X22)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_xt1_I1_J) ).

fof(fact_57_xt1_I2_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
         => ( ti(X1,X22) = ti(X1,X37)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_xt1_I2_J) ).

fof(fact_785_Un__absorb1,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_Un__absorb1) ).

fof(fact_784_subset__Un__eq,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
    <=> hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_subset__Un__eq) ).

fof(fact_786_Un__absorb2,axiom,
    ! [X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
     => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_Un__absorb2) ).

fof(fact_912_Int__absorb2,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_Int__absorb2) ).

fof(fact_911_Int__absorb1,axiom,
    ! [X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
     => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = ti(fun(X1,bool),X43) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_Int__absorb1) ).

fof(fact_127_xt1_I11_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
         => ( ti(X1,X21) != ti(X1,X22)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_xt1_I11_J) ).

fof(fact_126_order__le__neq__trans,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( ti(X1,X21) != ti(X1,X22)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__le__neq__trans) ).

fof(fact_125_order__le__imp__less__or__eq,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
            | ti(X1,X34) = ti(X1,X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order__le__imp__less__or__eq) ).

fof(fact_120_order__neq__le__trans,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X21,X22] :
          ( ti(X1,X21) != ti(X1,X22)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_order__neq__le__trans) ).

fof(fact_116_order__le__less,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
            | ti(X1,X6) = ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_order__le__less) ).

fof(fact_114_order__less__le,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
            & ti(X1,X6) != ti(X1,X7) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_order__less__le) ).

fof(fact_121_xt1_I12_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X21,X22] :
          ( ti(X1,X21) != ti(X1,X22)
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_xt1_I12_J) ).

fof(fact_145_inj__eq,axiom,
    ! [X1,X2,X6,X7,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
      <=> ti(X1,X6) = ti(X1,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_inj__eq) ).

fof(fact_146_injD,axiom,
    ! [X1,X2,X6,X7,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hAPP(X1,X2,X38,X6) = hAPP(X1,X2,X38,X7)
       => ti(X1,X6) = ti(X1,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_injD) ).

fof(fact_369_ex__least__nat__le,axiom,
    ! [X30,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X30))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X30))
            & ! [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/sandbox/benchmark/theBenchmark.p',fact_369_ex__least__nat__le) ).

fof(fact_302_ex__new__if__finite,axiom,
    ! [X1,X40] :
      ( ~ 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),X40))
       => ? [X19] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_ex__new__if__finite) ).

fof(fact_541_Ints__double__eq__0__iff,axiom,
    ! [X1] :
      ( ring_char_0(X1)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
         => ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
          <=> ti(X1,X14) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_Ints__double__eq__0__iff) ).

fof(fact_317_inj__onI,axiom,
    ! [X2,X1,X38,X40] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X46),X40))
           => ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
             => ti(X1,X26) = ti(X1,X46) ) ) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_inj__onI) ).

fof(tsy_c_Finite__Set_Ofold__image_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofold__image_res) ).

fof(fact_73_linorder__neq__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ti(X1,X6) != ti(X1,X7)
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
            | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_linorder__neq__iff) ).

fof(fact_71_linorder__less__linear,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
          | ti(X1,X34) = ti(X1,X35)
          | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_linorder__less__linear) ).

fof(fact_734_o__eq__dest__lhs,axiom,
    ! [X1,X3,X2,X107,X14,X15,X17] :
      ( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = ti(fun(X1,X2),X17)
     => hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X1,X2,X17,X107) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_o__eq__dest__lhs) ).

fof(fact_844_sup__absorb2,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_sup__absorb2) ).

fof(fact_840_le__iff__sup,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
        <=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7) = ti(X1,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_le__iff__sup) ).

fof(fact_845_sup__absorb1,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = ti(X1,X34) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_sup__absorb1) ).

fof(fact_929_le__iff__inf,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
        <=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = ti(X1,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_le__iff__inf) ).

fof(fact_925_inf__absorb1,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X34) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_inf__absorb1) ).

fof(fact_924_inf__absorb2,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = ti(X1,X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_inf__absorb2) ).

fof(fact_22_Pair__eq,axiom,
    ! [X2,X1,X14,X15,X12,X13] :
      ( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X12),X13)
    <=> ( ti(X1,X14) = ti(X1,X12)
        & ti(X2,X15) = ti(X2,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

fof(fact_21_Pair__inject,axiom,
    ! [X2,X1,X21,X22,X23,X24] :
      ( hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X21),X22) = hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X23),X24)
     => ~ ( ti(X1,X21) = ti(X1,X23)
         => ti(X2,X22) != ti(X2,X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

fof(fact_715_UNIV__eq__I,axiom,
    ! [X1,X40] :
      ( ! [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
     => top_top(fun(X1,bool)) = ti(fun(X1,bool),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_UNIV__eq__I) ).

fof(tsy_c_FuncSet_Ocompose_res,axiom,
    ! [X1,X3,X2] : ti(fun(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)))),compose(X1,X3,X2)) = compose(X1,X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_FuncSet_Ocompose_res) ).

fof(fact_68_less__imp__neq,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ti(X1,X34) != ti(X1,X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__imp__neq) ).

fof(fact_65_order__less__imp__not__eq,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ti(X1,X34) != ti(X1,X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_order__less__imp__not__eq) ).

fof(fact_64_order__less__imp__not__eq2,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ti(X1,X35) != ti(X1,X34) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__less__imp__not__eq2) ).

fof(fact_154_injI,axiom,
    ! [X1,X2,X38] :
      ( ! [X26,X46] :
          ( hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X38,X46)
         => ti(X1,X26) = ti(X1,X46) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_injI) ).

fof(fact_95_linorder__le__cases,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_linorder__le__cases) ).

fof(fact_117_leI,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_leI) ).

fof(fact_118_not__leE,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X35,X34] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_not__leE) ).

fof(fact_210_equalityD1,axiom,
    ! [X1,X40,X43] :
      ( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_equalityD1) ).

fof(fact_209_equalityD2,axiom,
    ! [X1,X40,X43] :
      ( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_equalityD2) ).

fof(tsy_c_Finite__Set_Ofolding__idem_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__idem_res) ).

fof(tsy_c_Wellfounded_Omlex__prod_res,axiom,
    ! [X1] : ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Wellfounded_Omlex__prod_res) ).

fof(tsy_c_FuncSet_OPi_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_FuncSet_OPi_res) ).

fof(fact_217_linorder__neqE__nat,axiom,
    ! [X34,X35] :
      ( X34 != X35
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_linorder__neqE__nat) ).

fof(fact_168_add__right__cancel,axiom,
    ! [X1] :
      ( cancel_semigroup_add(X1)
     => ! [X15,X14,X17] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)
        <=> ti(X1,X15) = ti(X1,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_add__right__cancel) ).

fof(fact_165_add__right__imp__eq,axiom,
    ! [X1] :
      ( cancel_semigroup_add(X1)
     => ! [X22,X21,X37] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X21) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)
         => ti(X1,X22) = ti(X1,X37) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_add__right__imp__eq) ).

fof(fact_166_add__imp__eq,axiom,
    ! [X1] :
      ( cancel146912293up_add(X1)
     => ! [X21,X22,X37] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
         => ti(X1,X22) = ti(X1,X37) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_add__imp__eq) ).

fof(fact_169_add__left__cancel,axiom,
    ! [X1] :
      ( cancel_semigroup_add(X1)
     => ! [X14,X15,X17] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)
        <=> ti(X1,X15) = ti(X1,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_add__left__cancel) ).

fof(fact_167_add__left__imp__eq,axiom,
    ! [X1] :
      ( cancel_semigroup_add(X1)
     => ! [X21,X22,X37] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)
         => ti(X1,X22) = ti(X1,X37) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_add__left__imp__eq) ).

fof(fact_75_ext,axiom,
    ! [X1,X2,X38,X39] :
      ( ! [X26] : hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26)
     => ti(fun(X1,X2),X38) = ti(fun(X1,X2),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).

fof(fact_31_less__top,axiom,
    ! [X1] :
      ( top(X1)
     => ! [X14] :
          ( ti(X1,X14) != top_top(X1)
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),top_top(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_less__top) ).

fof(fact_529_surj__def,axiom,
    ! [X2,X1,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
    <=> ! [X46] :
        ? [X26] : ti(X1,X46) = hAPP(X2,X1,X38,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_surj__def) ).

fof(fact_527_surjD,axiom,
    ! [X2,X1,X7,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => ? [X26] : ti(X1,X7) = hAPP(X2,X1,X38,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_surjD) ).

fof(fact_526_surjE,axiom,
    ! [X2,X1,X7,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => ~ ! [X26] : ti(X1,X7) != hAPP(X2,X1,X38,X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_surjE) ).

fof(fact_134_top__le,axiom,
    ! [X1] :
      ( top(X1)
     => ! [X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X21))
         => ti(X1,X21) = top_top(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_top__le) ).

fof(fact_133_top__unique,axiom,
    ! [X1] :
      ( top(X1)
     => ! [X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X14))
        <=> ti(X1,X14) = top_top(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_top__unique) ).

fof(fact_880_sup__inf__absorb,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_sup__inf__absorb) ).

fof(fact_881_inf__sup__absorb,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_inf__sup__absorb) ).

fof(fact_353_not__one__le__zero,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_not__one__le__zero) ).

fof(fact_355_not__one__less__zero,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_not__one__less__zero) ).

fof(fact_539_nat__case__0,axiom,
    ! [X1,X28,X86] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),zero_zero(nat)) = ti(X1,X28),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_nat__case__0) ).

fof(fact_30_not__top__less,axiom,
    ! [X1] :
      ( top(X1)
     => ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_not__top__less) ).

fof(fact_74_order__less__irrefl,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_order__less__irrefl) ).

fof(fact_331_less__nat__zero__code,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_less__nat__zero__code) ).

fof(fact_329_not__less0,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_not__less0) ).

fof(fact_319_less__zeroE,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_less__zeroE) ).

fof(fact_218_less__irrefl__nat,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_less__irrefl__nat) ).

fof(fact_215_less__not__refl,axiom,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__not__refl) ).

fof(help_fdisj_3_1_U,axiom,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119))
      | hBOOL(X118)
      | hBOOL(X119) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

fof(help_fconj_2_1_U,axiom,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
      | hBOOL(X118) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

fof(help_fconj_3_1_U,axiom,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
      | hBOOL(X119) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

fof(help_fequal_2_1_T,axiom,
    ! [X1,X34,X35] :
      ( ti(X1,X34) != ti(X1,X35)
      | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

fof(help_If_1_1_T,axiom,
    ! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X34),X35) = ti(X1,X34),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).

fof(help_If_2_1_T,axiom,
    ! [X1,X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X34),X35) = ti(X1,X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).

fof(tsy_c_Sum__Type_OPlus_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).

fof(fact_299_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
       => ti(fun(X1,bool),X40) = top_top(fun(X1,bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_card__eq__UNIV__imp__eq__UNIV) ).

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

fof(fact_452_add__0__iff,axiom,
    ! [X1] :
      ( semiri456707255roduct(X1)
     => ! [X15,X14] :
          ( ti(X1,X15) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X14)
        <=> ti(X1,X14) = zero_zero(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_add__0__iff) ).

fof(fact_596_mult__eq__0__iff,axiom,
    ! [X1] :
      ( ring_n68954251visors(X1)
     => ! [X14,X15] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15) = zero_zero(X1)
        <=> ( ti(X1,X14) = zero_zero(X1)
            | ti(X1,X15) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_mult__eq__0__iff) ).

fof(fact_595_no__zero__divisors,axiom,
    ! [X1] :
      ( no_zero_divisors(X1)
     => ! [X22,X21] :
          ( ti(X1,X21) != zero_zero(X1)
         => ( ti(X1,X22) != zero_zero(X1)
           => hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) != zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_no__zero__divisors) ).

fof(fact_594_divisors__zero,axiom,
    ! [X1] :
      ( no_zero_divisors(X1)
     => ! [X21,X22] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = zero_zero(X1)
         => ( ti(X1,X21) = zero_zero(X1)
            | ti(X1,X22) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_divisors__zero) ).

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

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

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

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

fof(fact_934_inf__eq__top__iff,axiom,
    ! [X1] :
      ( bounded_lattice_top(X1)
     => ! [X6,X7] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X6),X7) = top_top(X1)
        <=> ( ti(X1,X6) = top_top(X1)
            & ti(X1,X7) = top_top(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_inf__eq__top__iff) ).

fof(fact_894_Int__UNIV__left,axiom,
    ! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X43) = ti(fun(X1,bool),X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_Int__UNIV__left) ).

fof(tsy_c_Hilbert__Choice_Oinv__into_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hilbert__Choice_Oinv__into_res) ).

fof(tsy_c_Fun_Othe__inv__into_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Fun_Othe__inv__into_res) ).

fof(tsy_c_FuncSet_Orestrict_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_FuncSet_Orestrict_res) ).

fof(fact_985_setsum_Oinfinite,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X40] :
          ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_setsum_Oinfinite) ).

fof(fact_984_setsum__infinite,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X38,X40] :
          ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),X40) = zero_zero(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_setsum__infinite) ).

fof(tsy_c_FunDef_Oin__rel_res,axiom,
    ! [X1,X2] : ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_FunDef_Oin__rel_res) ).

fof(fact_893_Int__UNIV__right,axiom,
    ! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),top_top(fun(X1,bool))) = ti(fun(X1,bool),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_Int__UNIV__right) ).

fof(help_fconj_1_1_U,axiom,
    ! [X119,X118] :
      ( ~ hBOOL(X118)
      | ~ hBOOL(X119)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

fof(help_fdisj_1_1_U,axiom,
    ! [X119,X118] :
      ( ~ hBOOL(X118)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

fof(help_fdisj_2_1_U,axiom,
    ! [X118,X119] :
      ( ~ hBOOL(X119)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

fof(tsy_c_Set_Oimage_res,axiom,
    ! [X2,X1] : ti(fun(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool))),image(X2,X1)) = image(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).

fof(fact_429_double__eq__0__iff,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14) = zero_zero(X1)
        <=> ti(X1,X14) = zero_zero(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_double__eq__0__iff) ).

fof(fact_324_double__zero__sym,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)
        <=> ti(X1,X14) = zero_zero(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_double__zero__sym) ).

fof(fact_791_Un__absorb,axiom,
    ! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_Un__absorb) ).

fof(fact_908_Int__absorb,axiom,
    ! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X40) = ti(fun(X1,bool),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_Int__absorb) ).

fof(fact_466_image__ident,axiom,
    ! [X1,X80] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X80) = ti(fun(X1,bool),X80),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_image__ident) ).

fof(fact_534_greaterThan__eq__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X6) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)
        <=> ti(X1,X6) = ti(X1,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_greaterThan__eq__iff) ).

fof(fact_861_atLeast__eq__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X6) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)
        <=> ti(X1,X6) = ti(X1,X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_atLeast__eq__iff) ).

fof(tsy_c_Nat_Onat_Onat__case_res,axiom,
    ! [X1] : ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Onat_Onat__case_res) ).

fof(tsy_c_Wellfounded_Ofinite__psubset_res,axiom,
    ! [X1] : ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Wellfounded_Ofinite__psubset_res) ).

fof(tsy_c_hAPP_arg1,axiom,
    ! [X1,X3,X4,X5] : hAPP(X1,X3,ti(fun(X1,X3),X4),X5) = hAPP(X1,X3,X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).

fof(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ti(fun(fun(X1,X2),fun(fun(X1,bool),X2)),big_co1399186613setsum(X1,X2)) = big_co1399186613setsum(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) ).

fof(tsy_c_FuncSet_Oextensional_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_FuncSet_Oextensional_res) ).

fof(tsy_c_Fun_Oinj__on_res,axiom,
    ! [X1,X2] : ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Fun_Oinj__on_res) ).

fof(tsy_c_Wellfounded_Omeasure_res,axiom,
    ! [X1] : ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Wellfounded_Omeasure_res) ).

fof(help_COMBK_1_1_U,axiom,
    ! [X2,X1,X118,X119] : hAPP(X2,X1,hAPP(X1,fun(X2,X1),combk(X1,X2),X118),X119) = ti(X1,X118),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

fof(fact_936_inf__top__left,axiom,
    ! [X1] :
      ( bounded_lattice_top(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_inf__top__left) ).

fof(fact_613_mult__1,axiom,
    ! [X1] :
      ( comm_monoid_mult(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_mult__1) ).

fof(fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_612_mult__1__left,axiom,
    ! [X1] :
      ( monoid_mult(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_mult__1__left) ).

fof(fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_326_add__0__left,axiom,
    ! [X1] :
      ( monoid_add(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_add__0__left) ).

fof(fact_325_add__0,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_add__0) ).

fof(fact_935_inf__top__right,axiom,
    ! [X1] :
      ( bounded_lattice_top(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),top_top(X1)) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_inf__top__right) ).

fof(fact_615_mult_Ocomm__neutral,axiom,
    ! [X1] :
      ( comm_monoid_mult(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_mult_Ocomm__neutral) ).

fof(fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_614_mult__1__right,axiom,
    ! [X1] :
      ( monoid_mult(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),one_one(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_mult__1__right) ).

fof(fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_323_add__0__right,axiom,
    ! [X1] :
      ( monoid_add(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_add__0__right) ).

fof(fact_322_add_Ocomm__neutral,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),zero_zero(X1)) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_add_Ocomm__neutral) ).

fof(fact_976_Sup__fin_Oidem,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_Sup__fin_Oidem) ).

fof(fact_823_sup__idem,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_sup__idem) ).

fof(fact_822_sup_Oidem,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_sup_Oidem) ).

fof(fact_977_Inf__fin_Oidem,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_Inf__fin_Oidem) ).

fof(fact_952_inf_Oidem,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_inf_Oidem) ).

fof(fact_951_inf__idem,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_inf__idem) ).

fof(fact_820_mult__idem,axiom,
    ! [X1] :
      ( ab_sem1668676832m_mult(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34) = ti(X1,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_mult__idem) ).

fof(fact_819_times_Oidem,axiom,
    ! [X1] :
      ( ab_sem1668676832m_mult(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21) = ti(X1,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_times_Oidem) ).

fof(tsy_c_Product__Type_OPair_res,axiom,
    ! [X1,X2] : ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).

fof(help_ti_idem,axiom,
    ! [X116,X117] : ti(X116,ti(X116,X117)) = ti(X116,X117),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).

fof(tsy_c_hAPP_arg2,axiom,
    ! [X1,X3,X4,X5] : hAPP(X1,X3,X4,ti(X1,X5)) = hAPP(X1,X3,X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X3,X1,X4,X5] : ti(X3,hAPP(X1,X3,X4,X5)) = hAPP(X1,X3,X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

fof(tsy_c_If_res,axiom,
    ! [X1] : ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_If_res) ).

fof(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res,axiom,
    ! [X1] :
      ( linorder(X1)
     => ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res) ).

fof(tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res,axiom,
    ! [X1] :
      ( linorder(X1)
     => ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res,axiom,
    ! [X1] :
      ( linorder(X1)
     => ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) ).

fof(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res,axiom,
    ! [X1] :
      ( order(X1)
     => ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) ).

fof(tsy_c_member_res,axiom,
    ! [X1] : ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).

fof(fact_357_card__infinite,axiom,
    ! [X1,X40] :
      ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_card__infinite) ).

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

fof(help_fNot_1_1_U,axiom,
    ! [X118] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X118))
      | ~ hBOOL(X118) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

fof(tsy_c_Set_OCollect_res,axiom,
    ! [X1] : ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).

fof(fact_77_Collect__def,axiom,
    ! [X1,X11] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11) = ti(fun(X1,bool),X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).

fof(tsy_c_COMBK_res,axiom,
    ! [X1,X2] : ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).

fof(tsy_c_Lattices_Osemilattice__sup__class_Osup_res,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Lattices_Osemilattice__sup__class_Osup_res) ).

fof(tsy_c_Lattices_Osemilattice__inf__class_Oinf_res,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Lattices_Osemilattice__inf__class_Oinf_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_4_res,axiom,
    ! [X1] :
      ( no_zero_divisors(X1)
     => ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_3_res,axiom,
    ! [X1] :
      ( mult_zero(X1)
     => ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_2_res,axiom,
    ! [X1] :
      ( ab_semigroup_mult(X1)
     => ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_1_res,axiom,
    ! [X1] :
      ( monoid_mult(X1)
     => ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).

fof(tsy_c_Groups_Otimes__class_Otimes_0_res,axiom,
    ! [X1] :
      ( semiring(X1)
     => ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
    ! [X1] :
      ( cancel_semigroup_add(X1)
     => ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
    ! [X1] :
      ( ab_semigroup_add(X1)
     => ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
    ! [X1] :
      ( monoid_add(X1)
     => ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).

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

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

fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
    ! [X2] :
      ( ord(X2)
     => ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) = ord_less_eq(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).

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

fof(tsy_c_fequal_res,axiom,
    ! [X1] : ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).

fof(tsy_c_Finite__Set_Ocard_res,axiom,
    ! [X1] : ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).

fof(tsy_c_Finite__Set_Ofinite_res,axiom,
    ! [X2] : ti(fun(fun(X2,bool),bool),finite_finite_1(X2)) = finite_finite_1(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).

fof(help_fFalse_1_1_T,axiom,
    ! [X118] :
      ( ti(bool,X118) = fTrue
      | ti(bool,X118) = fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

fof(help_fTrue_1_1_T,axiom,
    ! [X118] :
      ( ti(bool,X118) = fTrue
      | ti(bool,X118) = fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

fof(help_If_3_1_T,axiom,
    ! [X118] :
      ( ti(bool,X118) = fTrue
      | ti(bool,X118) = fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).

fof(tsy_c_COMBI_res,axiom,
    ! [X1] : ti(fun(X1,X1),combi(X1)) = combi(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).

fof(tsy_c_Int_Oring__1__class_OInts_res,axiom,
    ! [X1] :
      ( ring_1(X1)
     => ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Oring__1__class_OInts_res) ).

fof(tsy_c_Orderings_Otop__class_Otop_res,axiom,
    ! [X1] :
      ( top(X1)
     => ti(X1,top_top(X1)) = top_top(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Otop__class_Otop_res) ).

fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
    ! [X1] :
      ( zero(X1)
     => ti(X1,zero_zero(X1)) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).

fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
    ! [X1] :
      ( one(X1)
     => ti(X1,one_one(X1)) = one_one(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).

fof(tsy_c_HOL_Oundefined_res,axiom,
    ! [X1] : ti(X1,undefined(X1)) = undefined(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

fof(fact_758_folding__image_Orelated,axiom,
    ! [X2,X1,X76,X39,X41,X42,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X9),X9))
       => ( ! [X18,X100,X101,X102] :
              ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
                & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,X101),X102))) )
         => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
           => ( ! [X26] :
                  ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X41)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_folding__image_Orelated) ).

fof(fact_83__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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    file('/export/starexec/sandbox/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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).

fof(fact_818_sup__Un__eq2,axiom,
    ! [X2,X1,X42,X41,X26,X27] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X42)),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)))),X41)),X26),X27))
    <=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X42),X41))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_sup__Un__eq2) ).

fof(fact_969_inf__Int__eq2,axiom,
    ! [X2,X1,X42,X41,X26,X27] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X42)),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)))),X41)),X26),X27))
    <=> 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),X26),X27)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X42),X41))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_inf__Int__eq2) ).

fof(fact_709_fold__image__related,axiom,
    ! [X2,X1] :
      ( comm_monoid_mult(X1)
     => ! [X76,X39,X41,X42,X99] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X99),X99))
         => ( ! [X18,X100,X101,X102] :
                ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X18),X101))
                  & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,X100),X102)) )
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X18),X100)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X101),X102))) )
           => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X41))
             => ( ! [X26] :
                    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X41))
                   => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(X2,X1,X76,X26)),hAPP(X2,X1,X39,X26))) )
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X42,hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X76),X99),X41)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X39),X99),X41))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_fold__image__related) ).

fof(fact_93__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_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
      & ! [X33] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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/sandbox/benchmark/theBenchmark.p',fact_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).

fof(fact_46_n_I2_J,axiom,
    ! [X33] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),n))
     => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_n_I2_J) ).

fof(fact_42_PiProf,axiom,
    ! [X30] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X30))),lab)),lba)),arrow_301600364e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_PiProf) ).

fof(fact_161_pred__subset__eq2,axiom,
    ! [X1,X2,X42,X41] :
      ( 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)))),X42)),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)))),X41)))
    <=> 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)),X42),X41)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_pred__subset__eq2) ).

fof(fact_892_setsum__setsum__restrict,axiom,
    ! [X2,X1,X3] :
      ( comm_monoid_add(X3)
     => ! [X38,X42,X103,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X103))
           => hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,fun(X2,bool)),fun(X1,X3),hAPP(fun(X1,fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,bool)),fun(X1,X3)),combs(X1,fun(X2,bool),X3),hAPP(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3)),hAPP(fun(fun(X2,X3),fun(fun(X2,bool),X3)),fun(fun(X1,fun(X2,X3)),fun(X1,fun(fun(X2,bool),X3))),combb(fun(X2,X3),fun(fun(X2,bool),X3),X1),big_co1399186613setsum(X2,X3)),X38)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),collect(X2)),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X1),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X103)))),X42)))),X41) = hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),hAPP(fun(X2,fun(X1,bool)),fun(X2,X3),hAPP(fun(X2,fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,bool)),fun(X2,X3)),combs(X2,fun(X1,bool),X3),hAPP(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3)),hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),fun(fun(X2,fun(X1,X3)),fun(X2,fun(fun(X1,bool),X3))),combb(fun(X1,X3),fun(fun(X1,bool),X3),X2),big_co1399186613setsum(X1,X3)),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X38))),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),collect(X1)),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X2),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),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)),X41)))),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),X42))))),X103) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_setsum__setsum__restrict) ).

fof(fact_745_folding__image_Ocong,axiom,
    ! [X2,X1,X39,X76,X40,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => ( ! [X26] :
              ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40))
             => hAPP(X2,X1,X39,X26) = hAPP(X2,X1,X76,X26) )
         => hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_folding__image_Ocong) ).

fof(fact_983_setsum__product,axiom,
    ! [X2,X3,X1] :
      ( semiring_0(X1)
     => ! [X38,X40,X39,X43] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X39),X43)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),hAPP(fun(X3,X1),fun(X2,fun(X3,X1)),hAPP(fun(X2,fun(fun(X3,X1),fun(X3,X1))),fun(fun(X3,X1),fun(X2,fun(X3,X1))),combc(X2,fun(X3,X1),fun(X3,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1))),hAPP(fun(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X3,X1),fun(X3,X1)))),combb(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),X2),combb(X1,X1,X3)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38))),X39))),X43)),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_setsum__product) ).

fof(fact_426_card__less__Suc,axiom,
    ! [X29,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)),X29))))) = 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,X29))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_card__less__Suc) ).

fof(fact_891_setsum__image__gen,axiom,
    ! [X3,X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X38,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X41) = hAPP(fun(X3,bool),X2,hAPP(fun(X3,X2),fun(fun(X3,bool),X2),big_co1399186613setsum(X3,X2),hAPP(fun(X3,fun(X1,bool)),fun(X3,X2),hAPP(fun(fun(X1,bool),X2),fun(fun(X3,fun(X1,bool)),fun(X3,X2)),combb(fun(X1,bool),X2,X3),hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),collect(X1)),hAPP(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool)),hAPP(fun(fun(X1,bool),fun(X1,bool)),fun(fun(X3,fun(X1,bool)),fun(X3,fun(X1,bool))),combb(fun(X1,bool),fun(X1,bool),X3),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),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)),X41)))),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X38)))))),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X41)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_setsum__image__gen) ).

fof(fact_917_setsum__restrict__set_H,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X38,X43,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),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)),X43)))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_setsum__restrict__set_H) ).

fof(fact_994_setsum__restrict__set,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X38,X43,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(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)),X43))),X38)),zero_zero(X2))),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_setsum__restrict__set) ).

fof(fact_916_setsum__restrict__set_H_H,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X38,X11,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),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),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)),X40))),X11))) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X11)),X38)),zero_zero(X2))),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_setsum__restrict__set_H_H) ).

fof(fact_887_if__image__distrib,axiom,
    ! [X2,X1,X11,X38,X39,X41] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),X11)),X38)),X39)),X41) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),X11)))),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X41),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(bool,bool),fun(fun(X2,bool),fun(X2,bool)),combb(bool,bool,X2),fNot),X11))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_if__image__distrib) ).

fof(fact_188_xt4,axiom,
    ! [X2,X1] :
      ( ( order(X1)
        & order(X2) )
     => ! [X17,X38,X15,X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X15)),X14))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_xt4) ).

fof(fact_187_xt6,axiom,
    ! [X2,X1] :
      ( ( order(X1)
        & ord(X2) )
     => ! [X17,X38,X15,X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X15)),X14))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X46)),hAPP(X2,X1,X38,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X17)),X14)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_xt6) ).

fof(fact_191_order__le__less__subst2,axiom,
    ! [X1,X2] :
      ( ( order(X2)
        & order(X1) )
     => ! [X38,X17,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
                 => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
             => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_order__le__less__subst2) ).

fof(fact_192_order__less__le__subst2,axiom,
    ! [X1,X2] :
      ( ( order(X2)
        & order(X1) )
     => ! [X38,X17,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
                 => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X38,X46))) )
             => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X14)),X17)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_order__less__le__subst2) ).

fof(fact_158_xt7,axiom,
    ! [X2,X1] :
      ( ( order(X1)
        & order(X2) )
     => ! [X17,X38,X15,X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
                 => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
             => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_xt7) ).

fof(fact_157_xt5,axiom,
    ! [X2,X1] :
      ( ( order(X1)
        & order(X2) )
     => ! [X17,X38,X15,X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X17),hAPP(X1,X2,X38,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
                 => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X38,X46)),hAPP(X1,X2,X38,X26))) )
             => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X17),hAPP(X1,X2,X38,X14))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_xt5) ).

fof(fact_190_order__less__le__subst1,axiom,
    ! [X1,X2] :
      ( ( order(X2)
        & order(X1) )
     => ! [X17,X14,X38,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X15)))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_order__less__le__subst1) ).

fof(fact_189_order__le__less__subst1,axiom,
    ! [X1,X2] :
      ( ( order(X2)
        & order(X1) )
     => ! [X17,X14,X38,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),hAPP(X2,X1,X38,X15)))
         => ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X38,X26)),hAPP(X2,X1,X38,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),hAPP(X2,X1,X38,X17))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_order__le__less__subst1) ).

fof(fact_427_card__less,axiom,
    ! [X29,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,X29))))) != zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_card__less) ).

fof(fact_697_fold__image__distrib,axiom,
    ! [X1,X2] :
      ( comm_monoid_mult(X2)
     => ! [X39,X76,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),times_times(X2)),X39)),X76)),one_one(X2)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),one_one(X2)),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_fold__image__distrib) ).

fof(fact_978_setsum__commute,axiom,
    ! [X2,X3,X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X43,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),X38)),X43)),X40) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X2,bool),fun(X3,X1),hAPP(fun(X3,fun(fun(X2,bool),X1)),fun(fun(X2,bool),fun(X3,X1)),combc(X3,fun(X2,bool),X1),hAPP(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1)),hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1))),combb(fun(X2,X1),fun(fun(X2,bool),X1),X3),big_co1399186613setsum(X2,X1)),hAPP(fun(X2,fun(X3,X1)),fun(X3,fun(X2,X1)),combc(X2,X3,X1),X38))),X40)),X43) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_setsum__commute) ).

fof(fact_866_fold__image__Un__Int,axiom,
    ! [X1,X2] :
      ( comm_monoid_mult(X2)
     => ! [X39,X43,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
           => hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X40)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),X43)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_fold__image__Un__Int) ).

fof(fact_23_IIA__def,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
         => ! [X27] :
              ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X27),arrow_301600364e_Prof))
             => ! [X19,X20] :
                  ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X27,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X27))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def) ).

fof(fact_290_finite__Collect__disjI,axiom,
    ! [X1,X11,X53] :
      ( 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),X11)),X53))))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_finite__Collect__disjI) ).

fof(fact_565_compose__assoc,axiom,
    ! [X87,X3,X1,X2,X76,X88,X39,X52,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
       => ( hBOOL(hAPP(fun(fun(X3,X87),bool),bool,hAPP(fun(X3,X87),fun(fun(fun(X3,X87),bool),bool),member(fun(X3,X87)),X76),hAPP(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X87,bool)),fun(fun(X3,X87),bool)),pi(X3,X87),X52),hAPP(fun(X87,bool),fun(X3,fun(X87,bool)),combk(fun(X87,bool),X3),X88))))
         => hAPP(fun(X1,X3),fun(X1,X87),hAPP(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X3,X87),fun(fun(X1,X3),fun(X1,X87))),compose(X1,X3,X87),X40),X76),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),X38)) = hAPP(fun(X1,X2),fun(X1,X87),hAPP(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87)),hAPP(fun(X1,bool),fun(fun(X2,X87),fun(fun(X1,X2),fun(X1,X87))),compose(X1,X2,X87),X40),hAPP(fun(X2,X3),fun(X2,X87),hAPP(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87)),hAPP(fun(X2,bool),fun(fun(X3,X87),fun(fun(X2,X3),fun(X2,X87))),compose(X2,X3,X87),X43),X76),X39)),X38) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_compose__assoc) ).

fof(fact_566_funcset__compose,axiom,
    ! [X3,X1,X2,X39,X52,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(fun(X2,X3),bool),bool,hAPP(fun(X2,X3),fun(fun(fun(X2,X3),bool),bool),member(fun(X2,X3)),X39),hAPP(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X3,bool)),fun(fun(X2,X3),bool)),pi(X2,X3),X43),hAPP(fun(X3,bool),fun(X2,fun(X3,bool)),combk(fun(X3,bool),X2),X52))))
       => hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X40),X39),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),X40),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X52)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_funcset__compose) ).

fof(fact_968_fold__image__Un__one,axiom,
    ! [X1,X2] :
      ( comm_monoid_mult(X2)
     => ! [X38,X103,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X103))
           => ( ! [X26] :
                  ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X41),X103)))
                 => hAPP(X1,X2,X38,X26) = one_one(X2) )
             => hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X41),X103)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X103)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_fold__image__Un__one) ).

fof(fact_301_finite__M__bounded__by__nat,axiom,
    ! [X11,X29] : 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)),X29))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_finite__M__bounded__by__nat) ).

fof(fact_737_inv__into__comp,axiom,
    ! [X1,X2,X3,X6,X38,X39,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
         => hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),hilbert_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_inv__into__comp) ).

fof(fact_738_the__inv__into__comp,axiom,
    ! [X1,X2,X3,X6,X38,X39,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40))))
         => hAPP(X2,X3,hAPP(fun(X3,X2),fun(X2,X3),hAPP(fun(X3,bool),fun(fun(X3,X2),fun(X2,X3)),the_inv_into(X3,X2),X40),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),X6) = hAPP(X2,X3,hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),comp(X1,X3,X2),hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),the_inv_into(X3,X1),X40),X39)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X39),X40)),X38)),X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_the__inv__into__comp) ).

fof(fact_804_sup__Un__eq,axiom,
    ! [X1,X42,X41,X26] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X42)),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)),X41)),X26))
    <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X42),X41))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_sup__Un__eq) ).

fof(fact_897_inf__Int__eq,axiom,
    ! [X1,X42,X41,X26] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X42)),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)),X41)),X26))
    <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X42),X41))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_inf__Int__eq) ).

fof(fact_258_Pi__mono,axiom,
    ! [X2,X1,X43,X52,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(X1,fun(X2,bool),X43,X26)),hAPP(X1,fun(X2,bool),X52,X26))) )
     => 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),X40),X43)),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),X40),X52))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Pi__mono) ).

fof(fact_272_Pi__cong,axiom,
    ! [X2,X1,X43,X38,X39,X40] :
      ( ! [X47] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X47),X40))
         => hAPP(X1,X2,X38,X47) = hAPP(X1,X2,X39,X47) )
     => ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
      <=> hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X39),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),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_Pi__cong) ).

fof(fact_886_Un__Int__crazy,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_Un__Int__crazy) ).

fof(fact_559_restrictI,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_restrictI) ).

fof(fact_701_fold__image__cong,axiom,
    ! [X1,X2] :
      ( ab_semigroup_mult(X2)
     => ! [X9,X39,X76,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => ( ! [X26] :
                ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
               => hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X76,X26) )
           => hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X39),X9),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X76),X9),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_fold__image__cong) ).

fof(fact_284_finite__Collect__conjI,axiom,
    ! [X1,X53,X11] :
      ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
        | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) )
     => 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),X11)),X53)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_finite__Collect__conjI) ).

fof(fact_314_finite__less__ub,axiom,
    ! [X66,X38] :
      ( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X38,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)),X38)),X66)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_finite__less__ub) ).

fof(fact_742_folding__image_Odistrib,axiom,
    ! [X2,X1,X39,X76,X40,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),X38),X39)),X76)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X76),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_folding__image_Odistrib) ).

fof(fact_273_Pi__I_H,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Pi__I_H) ).

fof(fact_149_Pi__I,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,fun(X2,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Pi__I) ).

fof(fact_918_image__Int__subset,axiom,
    ! [X1,X2,X38,X40,X43] : 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),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X40),X43))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_image__Int__subset) ).

fof(fact_532_Ints__odd__less__0,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(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)),X14)),X14)),zero_zero(X1)))
          <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_Ints__odd__less__0) ).

fof(fact_698_convex__bound__le,axiom,
    ! [X1] :
      ( linord1278240602ring_1(X1)
     => ! [X89,X90,X35,X34,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X21))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
               => ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_convex__bound__le) ).

fof(fact_570_convex__bound__lt,axiom,
    ! [X1] :
      ( linord626643107strict(X1)
     => ! [X89,X90,X35,X34,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X21))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X90))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X89))
               => ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X90),X89) = one_one(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),times_times(X1),X90),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X89),X35))),X21)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_convex__bound__lt) ).

fof(fact_560_restrict__in__funcset,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_restrict__in__funcset) ).

fof(fact_873_distrib__inf__le,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_distrib__inf__le) ).

fof(fact_792_Un__def,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_Un__def) ).

fof(fact_907_Int__def,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = 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),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)),X40))),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)),X43))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_Int__def) ).

fof(fact_867_setsum__ub__add__nat,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X113,X54,X30] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),one_one(nat))))
         => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X113)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_setsum__ub__add__nat) ).

fof(fact_306_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X2,X1,X43,X40,X38,X9,X39,X25] :
      ( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),X40))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X43)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_folding__image__simple__idem_Osubset__idem) ).

fof(fact_808_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X2,X1,X43,X40,X38,X9,X39,X25] :
      ( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
         => hAPP(fun(X2,bool),X1,X25,hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(fun(X2,bool),X1,X25,X40)),hAPP(fun(X2,bool),X1,X25,X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_folding__image__simple__idem_Ounion__idem) ).

fof(fact_270_funcsetI,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
     => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_funcsetI) ).

fof(fact_312_folding__image__simple__idem_Oin__idem,axiom,
    ! [X2,X1,X6,X40,X38,X9,X39,X25] :
      ( hBOOL(hAPP(fun(fun(X2,bool),X1),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool),hAPP(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool))),finite908156982e_idem(X1,X2),X38),X9),X39),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X40))
         => hAPP(X1,X1,hAPP(X1,fun(X1,X1),X38,hAPP(X2,X1,X39,X6)),hAPP(fun(X2,bool),X1,X25,X40)) = hAPP(fun(X2,bool),X1,X25,X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_folding__image__simple__idem_Oin__idem) ).

fof(fact_277_card__bij,axiom,
    ! [X1,X2,X39,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
       => ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X39),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),X43),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X40))))
         => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X39),X43))
           => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
             => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
               => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_card__bij) ).

fof(fact_530_image__subsetI,axiom,
    ! [X2,X1,X38,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X26)),X43)) )
     => 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),X38),X40)),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_image__subsetI) ).

fof(fact_24_unanimity__def,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
         => ! [X19,X20] :
              ( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X16)))
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X19),X20)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

fof(fact_508_card__bij__eq,axiom,
    ! [X1,X2,X39,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( 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),X38),X40)),X43))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),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(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X39),X43)),X40))
           => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
             => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
               => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X2,bool),nat,finite_card(X2),X43) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_card__bij__eq) ).

fof(fact_874_distrib__sup__le,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_distrib__sup__le) ).

fof(fact_989_setsum_Odistrib,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X76,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),plus_plus(X2)),X39)),X76)),X40) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X76),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_setsum_Odistrib) ).

fof(fact_980_setsum__addf,axiom,
    ! [X2,X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X39,X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),plus_plus(X1)),X38)),X39)),X40) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X39),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_setsum__addf) ).

fof(fact_525_inj__on__image__iff,axiom,
    ! [X2,X1,X39,X38,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => ! [X27] :
              ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X27),X40))
             => ( hAPP(X1,X2,X39,hAPP(X1,X1,X38,X26)) = hAPP(X1,X2,X39,hAPP(X1,X1,X38,X27))
              <=> hAPP(X1,X2,X39,X26) = hAPP(X1,X2,X39,X27) ) ) )
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
        <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_inj__on__image__iff) ).

fof(fact_753_mlex__leq,axiom,
    ! [X1,X42,X38,X6,X7] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
     => ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),X42))
       => hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_mlex__leq) ).

fof(fact_982_setsum__left__distrib,axiom,
    ! [X2,X1] :
      ( semiring_0(X1)
     => ! [X38,X40,X106] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)),X106) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X38)),X106)),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_setsum__left__distrib) ).

fof(fact_547_the__inv__into__into,axiom,
    ! [X1,X2,X43,X6,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38),X6)),X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_the__inv__into__into) ).

fof(fact_511_inj__transfer,axiom,
    ! [X1,X2,X6,X11,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( ! [X46] :
            ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X46),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)))))
           => hBOOL(hAPP(X1,bool,X11,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))),X38),X46))) )
       => hBOOL(hAPP(X1,bool,X11,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_inj__transfer) ).

fof(fact_668_Suc__mult__le__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_Suc__mult__le__cancel1) ).

fof(fact_665_Suc__mult__less__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_Suc__mult__less__cancel1) ).

fof(fact_214_pred__subset__eq,axiom,
    ! [X1,X42,X41] :
      ( 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)),X42)),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)),X41)))
    <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X42),X41)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_pred__subset__eq) ).

fof(fact_739_folding__image_Oreindex,axiom,
    ! [X2,X1,X39,X76,X40,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X2),fun(fun(X2,bool),bool),inj_on(X2,X2),X76),X40))
         => hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,bool)),image(X2,X2),X76),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,hAPP(fun(X2,X2),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X2),fun(X2,X1)),comp(X2,X1,X2),X39),X76)),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_folding__image_Oreindex) ).

fof(fact_672_compose__extensional,axiom,
    ! [X1,X2,X3,X40,X38,X39] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X38),X39)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_compose__extensional) ).

fof(fact_490_finite__range__imageI,axiom,
    ! [X3,X1,X2,X38,X39] :
      ( 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),X39),top_top(fun(X2,bool)))))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),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),X38),X39)),top_top(fun(X2,bool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_finite__range__imageI) ).

fof(fact_718_fold__image__reindex,axiom,
    ! [X2,X1,X3] :
      ( ab_semigroup_mult(X3)
     => ! [X39,X9,X76,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X76),X40))
           => hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X39),X9),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X76),X40)) = hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X76)),X9),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_fold__image__reindex) ).

fof(fact_746_in__finite__psubset,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X40),X43)),finite_psubset(X1)))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_in__finite__psubset) ).

fof(fact_744_folding__image_Oeq__fold,axiom,
    ! [X2,X1,X39,X40,X38,X9,X25] :
      ( hBOOL(hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool,hAPP(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)),finite_folding_image(X1,X2),X38),X9),X25))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40))
       => hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),X25,X39),X40) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),X38),X39),X9),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_folding__image_Oeq__fold) ).

fof(fact_475_inv__into__into,axiom,
    ! [X1,X2,X6,X38,X40] :
      ( 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),X38),X40)))
     => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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),X40),X38),X6)),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_inv__into__into) ).

fof(fact_260_mono__nat__linear__lb,axiom,
    ! [X54,X57,X38] :
      ( ! [X33,X44] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X44))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X38,X33)),hAPP(nat,nat,X38,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,X38,X54)),X57)),hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_mono__nat__linear__lb) ).

fof(fact_434_lift__Suc__mono__less__iff,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X30,X54,X38] :
          ( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X54)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_lift__Suc__mono__less__iff) ).

fof(fact_492_funcset__image,axiom,
    ! [X1,X2,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => 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),X38),X40)),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_funcset__image) ).

fof(fact_497_inj__image__subset__iff,axiom,
    ! [X1,X2,X40,X43,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( 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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)))
      <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_inj__image__subset__iff) ).

fof(fact_433_lift__Suc__mono__le,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X30,X72,X38] :
          ( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X72))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_lift__Suc__mono__le) ).

fof(fact_435_lift__Suc__mono__less,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X30,X72,X38] :
          ( ! [X44] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X44)),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X72))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X38,X30)),hAPP(nat,X1,X38,X72))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_lift__Suc__mono__less) ).

fof(fact_890_setsum__shift__bounds__nat__ivl,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_setsum__shift__bounds__nat__ivl) ).

fof(fact_888_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X57,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_995_setsum__Un__Int,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X43,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
           => hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_setsum__Un__Int) ).

fof(fact_724_comp__inj__on__iff,axiom,
    ! [X3,X1,X2,X105,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X105),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
      <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X105),X38)),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_comp__inj__on__iff) ).

fof(fact_617_combine__common__factor,axiom,
    ! [X1] :
      ( semiring(X1)
     => ! [X21,X96,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X96)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X96)),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X96)),X37) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_combine__common__factor) ).

fof(fact_489_subset__card__intvl__is__intvl,axiom,
    ! [X40,X57] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X40),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),X40)))))
     => X40 = 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),X40))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_subset__card__intvl__is__intvl) ).

fof(fact_975_inf2D1,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_inf2D1) ).

fof(fact_974_inf2D2,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_inf2D2) ).

fof(fact_274_card__inj,axiom,
    ! [X1,X2,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
       => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_card__inj) ).

fof(fact_510_inj__on__iff__card__le,axiom,
    ! [X2,X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
       => ( ? [X84] :
              ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X84),X40))
              & 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),X84),X40)),X43)) )
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_inj__on__iff__card__le) ).

fof(fact_708_left__add__mult__distrib,axiom,
    ! [X58,X90,X59,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X90)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X90)),X50)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X90)),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_left__add__mult__distrib) ).

fof(fact_509_card__inj__on__le,axiom,
    ! [X1,X2,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( 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),X38),X40)),X43))
       => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_card__inj__on__le) ).

fof(fact_143_funcset__mem,axiom,
    ! [X1,X2,X6,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X43))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_funcset__mem) ).

fof(fact_722_inj__on__imageI,axiom,
    ! [X1,X2,X3,X39,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X39),X38)),X40))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),X39),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),X40))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_inj__on__imageI) ).

fof(fact_160_Pi__anti__mono,axiom,
    ! [X2,X1,X43,X48,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X48),X40))
     => 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),X40),X43)),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),X48),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Pi__anti__mono) ).

fof(fact_723_comp__inj__on,axiom,
    ! [X3,X1,X2,X39,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X39),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X39),X38)),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_comp__inj__on) ).

fof(fact_955_setsum__add__nat__ivl,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X113,X54,X30] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X113))
           => hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X30),X113))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_setsum__add__nat__ivl) ).

fof(fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff) ).

fof(fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff) ).

fof(fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_gr676655987ssThan(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff) ).

fof(fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff) ).

fof(fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_gr1471790799AtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff) ).

fof(fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff) ).

fof(fact_685_sum__squares__ge__zero,axiom,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X34,X35] : 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_sum__squares__ge__zero) ).

fof(fact_754_mlex__less,axiom,
    ! [X1,X42,X38,X6,X7] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7)))
     => hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X38),X42))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_mlex__less) ).

fof(fact_491_atLeastLessThan__subset__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X14,X15,X17,X81] :
          ( 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),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X17),X81)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14))
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_atLeastLessThan__subset__iff) ).

fof(fact_498_card__image__le,axiom,
    ! [X2,X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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),X38),X40))),hAPP(fun(X1,bool),nat,finite_card(X1),X40))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_card__image__le) ).

fof(fact_748_in__measure,axiom,
    ! [X1,X6,X7,X38] :
      ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X7)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X38)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X38,X6)),hAPP(X1,nat,X38,X7))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_in__measure) ).

fof(fact_788_Un__mono,axiom,
    ! [X1,X43,X88,X40,X52] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
       => 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X88))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_Un__mono) ).

fof(fact_909_Int__mono,axiom,
    ! [X1,X43,X88,X40,X52] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X88))
       => 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X88))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_Int__mono) ).

fof(fact_973_inf2I,axiom,
    ! [X2,X1,X43,X40,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
     => ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_inf2I) ).

fof(fact_139_Pi__mem,axiom,
    ! [X1,X2,X6,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Pi__mem) ).

fof(fact_488_inj__on__strict__subset,axiom,
    ! [X1,X2,X40,X38,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
       => 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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_inj__on__strict__subset) ).

fof(fact_298_finite__Collect__not,axiom,
    ! [X1,X11] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)))
     => ( 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),X11))))
      <=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_finite__Collect__not) ).

fof(fact_683_mult__right__le__imp__le,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X21,X37,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_mult__right__le__imp__le) ).

fof(fact_684_mult__left__le__imp__le,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_mult__left__le__imp__le) ).

fof(fact_673_mult__le__cancel__left__pos,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15,X17] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
          <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_mult__le__cancel__left__pos) ).

fof(fact_679_mult__right__less__imp__less,axiom,
    ! [X1] :
      ( linordered_semiring(X1)
     => ! [X21,X37,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_mult__right__less__imp__less) ).

fof(fact_680_mult__less__imp__less__right,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X21,X37,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_mult__less__imp__less__right) ).

fof(fact_681_mult__left__less__imp__less,axiom,
    ! [X1] :
      ( linordered_semiring(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_mult__left__less__imp__less) ).

fof(fact_682_mult__less__imp__less__left,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_mult__less__imp__less__left) ).

fof(fact_639_mult__less__cancel__left__pos,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15,X17] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
          <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_mult__less__cancel__left__pos) ).

fof(fact_674_mult__le__cancel__left__neg,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15,X17] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
          <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_mult__le__cancel__left__neg) ).

fof(fact_645_mult__less__cancel__left__neg,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15,X17] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
          <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_mult__less__cancel__left__neg) ).

fof(fact_726_inj__on__imageI2,axiom,
    ! [X1,X2,X3,X105,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X105),X38)),X40))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_inj__on__imageI2) ).

fof(fact_503_inj__on__inv__into,axiom,
    ! [X1,X2,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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),X40),X38)),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_inj__on__inv__into) ).

fof(fact_632_mult__mono_H,axiom,
    ! [X1] :
      ( ordered_semiring(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_mult__mono_H) ).

fof(fact_633_mult__mono,axiom,
    ! [X1] :
      ( ordered_semiring(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_mult__mono) ).

fof(fact_677_mult__less__le__imp__less,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_mult__less__le__imp__less) ).

fof(fact_678_mult__le__less__imp__less,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_mult__le__less__imp__less) ).

fof(fact_676_mult__strict__mono_H,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_mult__strict__mono_H) ).

fof(fact_675_mult__strict__mono,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X45))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_mult__strict__mono) ).

fof(fact_269_in__rel__def,axiom,
    ! [X2,X1,X42,X6,X7] :
      ( 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),X42),X6),X7))
    <=> 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),X6),X7)),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_in__rel__def) ).

fof(fact_695_mult__le__cancel2,axiom,
    ! [X54,X57,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_mult__le__cancel2) ).

fof(fact_704_nat__mult__le__cancel1,axiom,
    ! [X54,X30,X57] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_nat__mult__le__cancel1) ).

fof(fact_696_mult__le__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_mult__le__cancel1) ).

fof(fact_705_nat__mult__less__cancel1,axiom,
    ! [X54,X30,X57] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_nat__mult__less__cancel1) ).

fof(fact_957_inj__on__image__Int,axiom,
    ! [X1,X2,X43,X40,X38,X52] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X52))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
         => hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_inj__on__image__Int) ).

fof(fact_638_mult__less__cancel__left__disj,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X17),X15)))
        <=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_mult__less__cancel__left__disj) ).

fof(fact_637_mult__less__cancel__right__disj,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X15),X17)))
        <=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X17))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X14)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_mult__less__cancel__right__disj) ).

fof(fact_278_finite__Collect__subsets,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => 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))),X40)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_finite__Collect__subsets) ).

fof(fact_963_card_Ounion__inter,axiom,
    ! [X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_card_Ounion__inter) ).

fof(fact_962_card__Un__Int,axiom,
    ! [X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_card__Un__Int) ).

fof(fact_90_inj__fun,axiom,
    ! [X3,X1,X2,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,bool),bool),inj_on(X1,fun(X3,X2)),hAPP(fun(X1,X2),fun(X1,fun(X3,X2)),hAPP(fun(X2,fun(X3,X2)),fun(fun(X1,X2),fun(X1,fun(X3,X2))),combb(X2,fun(X3,X2),X1),combk(X2,X3)),X38)),top_top(fun(X1,bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_inj__fun) ).

fof(fact_858_sup2I1,axiom,
    ! [X2,X1,X43,X40,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_sup2I1) ).

fof(fact_859_sup2I2,axiom,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_sup2I2) ).

fof(fact_49_mktop__Lin,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X8),X6)),arrow_1568854078le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mktop__Lin) ).

fof(fact_50_mkbot__Lin,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X8),X6)),arrow_1568854078le_Lin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mkbot__Lin) ).

fof(fact_551_inj__on__restrict__eq,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),X40))
    <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_inj__on__restrict__eq) ).

fof(fact_721_inj__comp,axiom,
    ! [X3,X1,X2,X39,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X39),top_top(fun(X3,bool))))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(X3,X2),hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),comp(X1,X2,X3),X38),X39)),top_top(fun(X3,bool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_inj__comp) ).

fof(fact_178_add__le__cancel__right,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_add__le__cancel__right) ).

fof(fact_173_add__le__imp__le__right,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X21,X37,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_add__le__imp__le__right) ).

fof(fact_177_add__le__cancel__left,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_add__le__cancel__left) ).

fof(fact_172_add__le__imp__le__left,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_add__le__imp__le__left) ).

fof(fact_185_add__less__cancel__right,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X17)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X15),X17)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__less__cancel__right) ).

fof(fact_180_add__less__imp__less__right,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X21,X37,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add__less__imp__less__right) ).

fof(fact_184_add__less__cancel__left,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X14)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X17),X15)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__less__cancel__left) ).

fof(fact_179_add__less__imp__less__left,axiom,
    ! [X1] :
      ( ordere236663937imp_le(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22)))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_add__less__imp__less__left) ).

fof(fact_805_Collect__disj__eq,axiom,
    ! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_Collect__disj__eq) ).

fof(fact_895_Collect__conj__eq,axiom,
    ! [X1,X11,X53] : 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),X11)),X53)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_Collect__conj__eq) ).

fof(fact_462_image__mono,axiom,
    ! [X2,X1,X38,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => 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),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_image__mono) ).

fof(fact_556_inj__on__the__inv__into,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X40),X38)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_inj__on__the__inv__into) ).

fof(fact_663_mult__less__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_mult__less__cancel1) ).

fof(fact_662_mult__less__cancel2,axiom,
    ! [X54,X57,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_mult__less__cancel2) ).

fof(fact_250_nat__add__left__cancel__le,axiom,
    ! [X57,X54,X30] :
      ( 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),X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_nat__add__left__cancel__le) ).

fof(fact_235_nat__add__left__cancel__less,axiom,
    ! [X57,X54,X30] :
      ( 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),X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_nat__add__left__cancel__less) ).

fof(fact_186_le__funI,axiom,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X38,X39] :
          ( ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)))
         => hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_le__funI) ).

fof(fact_110_le__fun__def,axiom,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X38,X39] :
          ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
        <=> ! [X26] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_le__fun__def) ).

fof(fact_798_bex__Un,axiom,
    ! [X1,X11,X40,X43] :
      ( ? [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
          & hBOOL(hAPP(X1,bool,X11,X26)) )
    <=> ( ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
            & hBOOL(hAPP(X1,bool,X11,X26)) )
        | ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
            & hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_bex__Un) ).

fof(fact_799_ball__Un,axiom,
    ! [X1,X11,X40,X43] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
         => hBOOL(hAPP(X1,bool,X11,X26)) )
    <=> ( ! [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
           => hBOOL(hAPP(X1,bool,X11,X26)) )
        & ! [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43))
           => hBOOL(hAPP(X1,bool,X11,X26)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_ball__Un) ).

fof(conj_0,conjecture,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(fact_481_inj__image__mem__iff,axiom,
    ! [X1,X2,X14,X40,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
      <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_inj__image__mem__iff) ).

fof(fact_787_Un__least,axiom,
    ! [X1,X43,X40,X52] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
       => 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_Un__least) ).

fof(fact_694_one__le__mult__iff,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X54))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_one__le__mult__iff) ).

fof(fact_693_one__less__mult,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_one__less__mult) ).

fof(fact_52_const__Lin__Prof,axiom,
    ! [X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X8)),arrow_301600364e_Prof)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_const__Lin__Prof) ).

fof(fact_699_field__le__mult__one__interval,axiom,
    ! [X1] :
      ( linord1117847801e_zero(X1)
     => ! [X34,X35] :
          ( ! [X98] :
              ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X98))
             => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X98),one_one(X1)))
               => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X98),X34)),X35)) ) )
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_field__le__mult__one__interval) ).

fof(fact_875_Un__Int__assoc__eq,axiom,
    ! [X1,X40,X43,X52] :
      ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52))
    <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_Un__Int__assoc__eq) ).

fof(fact_318_inj__on__cong,axiom,
    ! [X2,X1,X38,X39,X40] :
      ( ! [X19] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40))
         => hAPP(X1,X2,X38,X19) = hAPP(X1,X2,X39,X19) )
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
      <=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X39),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_inj__on__cong) ).

fof(fact_960_setsum__head__upt__Suc,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X30] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
         => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_setsum__head__upt__Suc) ).

fof(fact_961_setsum__head__Suc,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X30] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
         => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X38,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),X30))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_setsum__head__Suc) ).

fof(fact_34_dictator__def,axiom,
    ! [X25,X29] :
      ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X25),X29))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X26),arrow_301600364e_Prof))
         => hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X25,X26) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X26,X29) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_dictator__def) ).

fof(fact_627_mult__right__mono,axiom,
    ! [X1] :
      ( ordered_semiring(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_mult__right__mono) ).

fof(fact_629_comm__mult__left__mono,axiom,
    ! [X1] :
      ( ordere1490568538miring(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_comm__mult__left__mono) ).

fof(fact_628_mult__left__mono,axiom,
    ! [X1] :
      ( ordered_semiring(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_mult__left__mono) ).

fof(fact_648_mult__strict__right__mono,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_mult__strict__right__mono) ).

fof(fact_650_comm__mult__strict__left__mono,axiom,
    ! [X1] :
      ( linord893533164strict(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_comm__mult__strict__left__mono) ).

fof(fact_649_mult__strict__left__mono,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_mult__strict__left__mono) ).

fof(fact_630_mult__right__mono__neg,axiom,
    ! [X1] :
      ( ordered_ring(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_mult__right__mono__neg) ).

fof(fact_631_mult__left__mono__neg,axiom,
    ! [X1] :
      ( ordered_ring(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_mult__left__mono__neg) ).

fof(fact_651_mult__strict__right__mono__neg,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_mult__strict__right__mono__neg) ).

fof(fact_652_mult__strict__left__mono__neg,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X37,X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X37),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_mult__strict__left__mono__neg) ).

fof(fact_848_sup__mono,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X22,X45,X21,X37] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X37),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_sup__mono) ).

fof(fact_921_inf__mono,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X22,X45,X21,X37] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X37))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X37),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_inf__mono) ).

fof(fact_174_add__mono,axiom,
    ! [X1] :
      ( ordere779506340up_add(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_add__mono) ).

fof(fact_152_add__less__le__mono,axiom,
    ! [X1] :
      ( ordere223160158up_add(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__less__le__mono) ).

fof(fact_153_add__le__less__mono,axiom,
    ! [X1] :
      ( ordere223160158up_add(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_add__le__less__mono) ).

fof(fact_181_add__strict__mono,axiom,
    ! [X1] :
      ( ordere223160158up_add(X1)
     => ! [X37,X45,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X37),X45))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add__strict__mono) ).

fof(fact_261_less__mono__imp__le__mono,axiom,
    ! [X29,X63,X38] :
      ( ! [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,X38,X16)),hAPP(nat,nat,X38,X64))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,X29)),hAPP(nat,nat,X38,X63))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_less__mono__imp__le__mono) ).

fof(fact_621_mult__le__0__iff,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)),zero_zero(X1)))
        <=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_mult__le__0__iff) ).

fof(fact_661_mult__less__mono1,axiom,
    ! [X50,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),zero_zero(nat)),X50))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_mult__less__mono1) ).

fof(fact_660_mult__less__mono2,axiom,
    ! [X50,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),zero_zero(nat)),X50))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_mult__less__mono2) ).

fof(fact_576_mult__le__mono,axiom,
    ! [X50,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),X50),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X61))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_mult__le__mono) ).

fof(fact_254_add__le__mono,axiom,
    ! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_add__le__mono) ).

fof(fact_239_add__less__mono,axiom,
    ! [X50,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),X50),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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_add__less__mono) ).

fof(fact_896_Int__Collect,axiom,
    ! [X1,X6,X40,X11] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X11))))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
        & hBOOL(hAPP(X1,bool,X11,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_Int__Collect) ).

fof(fact_692_n__less__n__mult__m,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_n__less__n__mult__m) ).

fof(fact_691_n__less__m__mult__n,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X49))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_n__less__m__mult__n) ).

fof(fact_690_mult__right__le__one__le,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),X34)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_mult__right__le__one__le) ).

fof(fact_689_mult__left__le__one__le,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X35))
           => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),one_one(X1)))
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X34)),X34)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_mult__left__le__one__le) ).

fof(fact_752_weak__decr__stable,axiom,
    ! [X38] :
      ( ! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X38,hAPP(nat,nat,suc,X16))),hAPP(nat,nat,X38,X16)))
     => ? [X16] :
        ! [X62] : hAPP(nat,nat,X38,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X62)) = hAPP(nat,nat,X38,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_weak__decr__stable) ).

fof(fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(fact_958_image__Int,axiom,
    ! [X1,X2,X40,X43,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_image__Int) ).

fof(fact_749_folding__idem_Oidem__left__comp,axiom,
    ! [X3,X1,X2,X6,X39,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
     => hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39)) = hAPP(fun(X3,X2),fun(X3,X2),hAPP(fun(X2,X2),fun(fun(X3,X2),fun(X3,X2)),comp(X2,X2,X3),hAPP(X1,fun(X2,X2),X38,X6)),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_folding__idem_Oidem__left__comp) ).

fof(fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_810_atLeastLessThan__add__Un,axiom,
    ! [X57,X29,X63] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X63))
     => hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X63),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_atLeastLessThan__add__Un) ).

fof(fact_345_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_350_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_371_even__less__0__iff,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X14] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X14),X14)),zero_zero(X1)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X14),zero_zero(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_even__less__0__iff) ).

fof(fact_841_le__sup__iff,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X6,X7,X9] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X6),X7)),X9))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9))
            & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X9)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_le__sup__iff) ).

fof(fact_571_Ints__mult,axiom,
    ! [X1] :
      ( ring_1(X1)
     => ! [X15,X14] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),ring_1_Ints(X1)))
           => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)),ring_1_Ints(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Ints__mult) ).

fof(fact_536_Ints__add,axiom,
    ! [X1] :
      ( ring_1(X1)
     => ! [X15,X14] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(X1)))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),ring_1_Ints(X1)))
           => 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),X14),X15)),ring_1_Ints(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_Ints__add) ).

fof(fact_885_Un__Int__distrib2,axiom,
    ! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X52),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_Un__Int__distrib2) ).

fof(fact_884_Int__Un__distrib2,axiom,
    ! [X1,X43,X52,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),X40) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X52),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_Int__Un__distrib2) ).

fof(fact_504_surj__imp__inj__inv,axiom,
    ! [X2,X1,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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),top_top(fun(X2,bool))),X38)),top_top(fun(X1,bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_surj__imp__inj__inv) ).

fof(fact_618_extensional__subset,axiom,
    ! [X1,X2,X43,X38,X40] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40)))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_extensional__subset) ).

fof(fact_279_card__psubset,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_card__psubset) ).

fof(fact_796_Un__iff,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
        | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_Un__iff) ).

fof(fact_533_less__eq__nat_Osimps_I2_J,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54)),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_less__eq__nat_Osimps_I2_J) ).

fof(fact_256_add__leD1,axiom,
    ! [X49,X50,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_add__leD1) ).

fof(fact_255_add__leD2,axiom,
    ! [X49,X50,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_add__leD2) ).

fof(fact_241_add__lessD1,axiom,
    ! [X58,X59,X50] :
      ( 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)),X50))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_add__lessD1) ).

fof(fact_176_add__right__mono,axiom,
    ! [X1] :
      ( ordere779506340up_add(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_add__right__mono) ).

fof(fact_175_add__left__mono,axiom,
    ! [X1] :
      ( ordere779506340up_add(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add__left__mono) ).

fof(fact_183_add__strict__right__mono,axiom,
    ! [X1] :
      ( ordere223160158up_add(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__strict__right__mono) ).

fof(fact_182_add__strict__left__mono,axiom,
    ! [X1] :
      ( ordere223160158up_add(X1)
     => ! [X37,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_add__strict__left__mono) ).

fof(fact_561_restrict__ext,axiom,
    ! [X2,X1,X38,X39,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hAPP(X1,X2,X38,X26) = hAPP(X1,X2,X39,X26) )
     => hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X39),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_restrict__ext) ).

fof(fact_967_card_Ounion__inter__neutral,axiom,
    ! [X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
           => one_one(nat) = zero_zero(nat) )
         => hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_card_Ounion__inter__neutral) ).

fof(fact_996_setsum_Oreindex,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X76,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X76),X40))
           => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X76),X40)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X39),X76)),X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_setsum_Oreindex) ).

fof(fact_981_setsum__right__distrib,axiom,
    ! [X2,X1] :
      ( semiring_0(X1)
     => ! [X106,X38,X40] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X106),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X38),X40)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X1,X1),fun(fun(X2,X1),fun(X2,X1)),combb(X1,X1,X2),hAPP(X1,fun(X1,X1),times_times(X1),X106)),X38)),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_setsum__right__distrib) ).

fof(fact_700_fold__image__1,axiom,
    ! [X1,X2] :
      ( comm_monoid_mult(X2)
     => ! [X38,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ! [X26] :
                ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X41))
               => hAPP(X1,X2,X38,X26) = one_one(X2) )
           => hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X38),one_one(X2)),X41) = one_one(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_fold__image__1) ).

fof(fact_919_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_setsum__shift__bounds__Suc__ivl) ).

fof(fact_889_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X54,X30] : hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X38),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_910_Int__greatest,axiom,
    ! [X1,X43,X52,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X52),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_Int__greatest) ).

fof(fact_574_mult__le__mono1,axiom,
    ! [X50,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),times_times(nat),X58),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X59),X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_mult__le__mono1) ).

fof(fact_575_mult__le__mono2,axiom,
    ! [X50,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),times_times(nat),X50),X58)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X59))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_mult__le__mono2) ).

fof(fact_253_add__le__mono1,axiom,
    ! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_add__le__mono1) ).

fof(fact_238_add__less__mono1,axiom,
    ! [X50,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),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add__less__mono1) ).

fof(fact_670_restrict__extensional,axiom,
    ! [X1,X2,X38,X40] : hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X38),X40)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X40))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_restrict__extensional) ).

fof(fact_493_finite__surj__inj,axiom,
    ! [X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X38),X40)))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_finite__surj__inj) ).

fof(fact_517_image__add__atLeastLessThan,axiom,
    ! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_image__add__atLeastLessThan) ).

fof(fact_768_image__add__atLeastAtMost,axiom,
    ! [X57,X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_image__add__atLeastAtMost) ).

fof(fact_635_split__mult__neg__le,axiom,
    ! [X1] :
      ( ordere453448008miring(X1)
     => ! [X22,X21] :
          ( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1))) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) ) )
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_split__mult__neg__le) ).

fof(fact_625_mult__nonpos__nonneg,axiom,
    ! [X1] :
      ( ordere453448008miring(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_mult__nonpos__nonneg) ).

fof(fact_623_mult__nonneg__nonpos,axiom,
    ! [X1] :
      ( ordere453448008miring(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_mult__nonneg__nonpos) ).

fof(fact_624_mult__nonneg__nonpos2,axiom,
    ! [X1] :
      ( ordere453448008miring(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_mult__nonneg__nonpos2) ).

fof(fact_646_mult__neg__pos,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_mult__neg__pos) ).

fof(fact_641_mult__pos__neg,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_mult__pos__neg) ).

fof(fact_642_mult__pos__neg2,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_mult__pos__neg2) ).

fof(fact_340_add__nonpos__nonpos,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_add__nonpos__nonpos) ).

fof(fact_359_add__neg__nonpos,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_add__neg__nonpos) ).

fof(fact_358_add__nonpos__neg,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_add__nonpos__neg) ).

fof(fact_347_add__neg__neg,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),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),X21),X22)),zero_zero(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_add__neg__neg) ).

fof(fact_847_sup__least,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X36,X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_sup__least) ).

fof(fact_846_le__supI,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X22,X21,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_le__supI) ).

fof(fact_915_inj__on__Int,axiom,
    ! [X1,X2,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_inj__on__Int) ).

fof(fact_991_setsum__reindex,axiom,
    ! [X1,X2,X3] :
      ( comm_monoid_add(X3)
     => ! [X76,X38,X43] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
         => hAPP(fun(X2,bool),X3,hAPP(fun(X2,X3),fun(fun(X2,bool),X3),big_co1399186613setsum(X2,X3),X76),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X43)) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X76),X38)),X43) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_setsum__reindex) ).

fof(fact_814_ivl__disj__un_I15_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_ivl__disj__un_I15_J) ).

fof(fact_772_ivl__disj__un_I19_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_ivl__disj__un_I19_J) ).

fof(fact_815_ivl__disj__un_I16_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_ivl__disj__un_I16_J) ).

fof(fact_778_ivl__disj__un_I20_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_ivl__disj__un_I20_J) ).

fof(fact_779_ivl__disj__un_I17_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_ivl__disj__un_I17_J) ).

fof(fact_809_ivl__disj__un_I21_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_ivl__disj__un_I21_J) ).

fof(fact_773_ivl__disj__un_I18_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_ivl__disj__un_I18_J) ).

fof(fact_811_ivl__disj__un_I22_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X66,X77,X54] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X54))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X54),X66))
           => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X54)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X54),X66)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_ivl__disj__un_I22_J) ).

fof(fact_747_folding__idem_Osubset__comp__idem,axiom,
    ! [X1,X2,X43,X40,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40))
         => hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_folding__idem_Osubset__comp__idem) ).

fof(fact_813_folding__idem_Ounion__idem,axiom,
    ! [X1,X2,X43,X40,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
         => hAPP(fun(X1,bool),fun(X2,X2),X25,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(fun(X1,bool),fun(X2,X2),X25,X43)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_folding__idem_Ounion__idem) ).

fof(fact_966_setsum__head,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X11,X54,X30] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
         => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X11,X54)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X11),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X54),X30))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_setsum__head) ).

fof(fact_144_funcset__id,axiom,
    ! [X1,X40] : 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),X40),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X40)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_funcset__id) ).

fof(fact_903_Int__iff,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
        & hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_Int__iff) ).

fof(fact_870_IntI,axiom,
    ! [X1,X43,X17,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_IntI) ).

fof(fact_751_folding__idem_Oin__comp__idem,axiom,
    ! [X1,X2,X6,X40,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
         => hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X25,X40)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(fun(X1,bool),fun(X2,X2),X25,X40) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_folding__idem_Oin__comp__idem) ).

fof(fact_901_IntD1,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_IntD1) ).

fof(fact_900_IntD2,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_IntD2) ).

fof(fact_456_card_Oeq__fold__g,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_card_Oeq__fold__g) ).

fof(fact_478_finite__surj,axiom,
    ! [X2,X1,X43,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X43),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40)))
       => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_finite__surj) ).

fof(fact_644_zero__less__mult__pos2,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_zero__less__mult__pos2) ).

fof(fact_643_zero__less__mult__pos,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_zero__less__mult__pos) ).

fof(fact_563_compose__eq,axiom,
    ! [X2,X3,X1,X39,X38,X6,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
     => hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38),X6) = hAPP(X3,X2,X39,hAPP(X1,X3,X38,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_compose__eq) ).

fof(fact_883_Un__Int__distrib,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_Un__Int__distrib) ).

fof(fact_882_Int__Un__distrib,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_Int__Un__distrib) ).

fof(fact_479_finite__imageD,axiom,
    ! [X1,X2,X38,X40] :
      ( 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),X38),X40)))
     => ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40))
       => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_finite__imageD) ).

fof(fact_232_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/sandbox/benchmark/theBenchmark.p',fact_232_inj__on__add__nat) ).

fof(fact_914_Int__lower1,axiom,
    ! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_Int__lower1) ).

fof(fact_913_Int__lower2,axiom,
    ! [X1,X40,X43] : 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X43)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_Int__lower2) ).

fof(fact_781_image__Un,axiom,
    ! [X2,X1,X38,X40,X43] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X43)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_image__Un) ).

fof(fact_283_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/sandbox/benchmark/theBenchmark.p',fact_283_finite__Collect__le__nat) ).

fof(fact_285_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/sandbox/benchmark/theBenchmark.p',fact_285_finite__Collect__less__nat) ).

fof(fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X22,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X95,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_469_imageI,axiom,
    ! [X2,X1,X38,X6,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
     => hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),X40))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_imageI) ).

fof(fact_573_le__cube,axiom,
    ! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_le__cube) ).

fof(fact_764_ex__nat__less,axiom,
    ! [X11,X30] :
      ( ? [X33] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
          & hBOOL(hAPP(nat,bool,X11,X33)) )
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
          & hBOOL(hAPP(nat,bool,X11,X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_ex__nat__less) ).

fof(fact_519_ex__nat__less__eq,axiom,
    ! [X11,X30] :
      ( ? [X33] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
          & hBOOL(hAPP(nat,bool,X11,X33)) )
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
          & hBOOL(hAPP(nat,bool,X11,X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_ex__nat__less__eq) ).

fof(fact_620_zero__le__mult__iff,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X14,X15] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X14),X15)))
        <=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X15)) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),zero_zero(X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_zero__le__mult__iff) ).

fof(fact_971_setsum_Oeq__fold,axiom,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X40] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_setsum_Oeq__fold) ).

fof(fact_765_all__nat__less,axiom,
    ! [X11,X30] :
      ( ! [X33] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X30))
         => hBOOL(hAPP(nat,bool,X11,X33)) )
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X30)))
         => hBOOL(hAPP(nat,bool,X11,X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_all__nat__less) ).

fof(fact_518_all__nat__less__eq,axiom,
    ! [X11,X30] :
      ( ! [X33] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X30))
         => hBOOL(hAPP(nat,bool,X11,X33)) )
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X30)))
         => hBOOL(hAPP(nat,bool,X11,X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_all__nat__less__eq) ).

fof(fact_927_le__infI1,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X22,X21,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_le__infI1) ).

fof(fact_926_le__infI2,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21,X22,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_le__infI2) ).

fof(fact_953_less__infI1,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X22,X21,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_less__infI1) ).

fof(fact_954_less__infI2,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21,X22,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_less__infI2) ).

fof(fact_729_o__assoc,axiom,
    ! [X1,X3,X2,X87,X38,X39,X76] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),hAPP(fun(X1,X87),fun(X1,X3),hAPP(fun(X87,X3),fun(fun(X1,X87),fun(X1,X3)),comp(X87,X3,X1),X39),X76)) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),hAPP(fun(X87,X3),fun(X87,X2),hAPP(fun(X3,X2),fun(fun(X87,X3),fun(X87,X2)),comp(X3,X2,X87),X38),X39)),X76),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_o__assoc) ).

fof(fact_356_add__gr__0,axiom,
    ! [X54,X30] :
      ( 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),X30)))
    <=> ( 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)),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_add__gr__0) ).

fof(fact_311_finite__Plus__iff,axiom,
    ! [X1,X2,X40,X43] :
      ( 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),X40),X43)))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
        & hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_finite__Plus__iff) ).

fof(fact_309_finite__PlusD_I1_J,axiom,
    ! [X1,X2,X40,X43] :
      ( 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),X40),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_finite__PlusD_I1_J) ).

fof(fact_308_finite__PlusD_I2_J,axiom,
    ! [X1,X2,X40,X43] :
      ( 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),X40),X43)))
     => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_finite__PlusD_I2_J) ).

fof(fact_567_compose__def,axiom,
    ! [X1,X3,X2,X40,X39,X38] : hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X40),X39),X38) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X39),X38)),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_compose__def) ).

fof(fact_257_predicate2I,axiom,
    ! [X2,X1,X53,X11] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X26),X46))
         => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X26),X46)) )
     => 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))),X11),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_predicate2I) ).

fof(fact_720_comp__surj,axiom,
    ! [X3,X2,X1,X39,X38] :
      ( hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))) = top_top(fun(X1,bool))
     => ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X39),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
       => 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)),comp(X1,X3,X2),X39),X38)),top_top(fun(X2,bool))) = top_top(fun(X3,bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_comp__surj) ).

fof(fact_542_greaterThan__subset__iff,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( 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),ord_greaterThan(X1),X6)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X7)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_greaterThan__subset__iff) ).

fof(fact_862_atLeast__subset__iff,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X6,X7] :
          ( 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),ord_atLeast(X1),X6)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X7)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_atLeast__subset__iff) ).

fof(fact_634_split__mult__pos__le,axiom,
    ! [X1] :
      ( ordered_ring(X1)
     => ! [X22,X21] :
          ( ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22)) )
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1))) ) )
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_split__mult__pos__le) ).

fof(fact_622_mult__nonneg__nonneg,axiom,
    ! [X1] :
      ( ordere453448008miring(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_mult__nonneg__nonneg) ).

fof(fact_344_add__nonneg__nonneg,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
           => 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),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_add__nonneg__nonneg) ).

fof(fact_640_mult__pos__pos,axiom,
    ! [X1] :
      ( linord20386208strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_mult__pos__pos) ).

fof(fact_363_add__pos__nonneg,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X22))
           => 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),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_add__pos__nonneg) ).

fof(fact_362_add__nonneg__pos,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
           => 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),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_add__nonneg__pos) ).

fof(fact_349_add__pos__pos,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X22))
           => 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),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_add__pos__pos) ).

fof(fact_655_less__1__mult,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => ! [X51,X49] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X49))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X51))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X49),X51))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_less__1__mult) ).

fof(fact_477_range__composition,axiom,
    ! [X2,X1,X3,X38,X39] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),combb(X3,X1,X2),X38),X39)),top_top(fun(X2,bool))) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),top_top(fun(X2,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_range__composition) ).

fof(fact_626_mult__nonpos__nonpos,axiom,
    ! [X1] :
      ( ordered_ring(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_mult__nonpos__nonpos) ).

fof(fact_647_mult__neg__neg,axiom,
    ! [X1] :
      ( linord581940658strict(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),zero_zero(X1)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),zero_zero(X1)))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_mult__neg__neg) ).

fof(fact_342_add__increasing,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X37,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_add__increasing) ).

fof(fact_341_add__increasing2,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X21,X37] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X37))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X21))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_add__increasing2) ).

fof(fact_361_add__strict__increasing,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X37,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_add__strict__increasing) ).

fof(fact_360_add__strict__increasing2,axiom,
    ! [X1] :
      ( ordere216010020id_add(X1)
     => ! [X22,X37,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_add__strict__increasing2) ).

fof(fact_348_pos__add__strict,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => ! [X22,X37,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X37))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_pos__add__strict) ).

fof(fact_928_le__inf__iff,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X6,X7,X9] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X7),X9)))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
            & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X9)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_le__inf__iff) ).

fof(fact_923_le__infI,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X22,X34,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_le__infI) ).

fof(fact_922_inf__greatest,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_inf__greatest) ).

fof(fact_454_field__le__epsilon,axiom,
    ! [X1] :
      ( linordered_field(X1)
     => ! [X34,X35] :
          ( ! [X75] :
              ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X75))
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X75))) )
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_field__le__epsilon) ).

fof(fact_467_image__image,axiom,
    ! [X2,X1,X3,X38,X39,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X39),X40)) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),combb(X2,X1,X3),X38),X39)),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_image__image) ).

fof(fact_725_image__compose,axiom,
    ! [X2,X1,X3,X38,X39,X106] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),comp(X3,X1,X2),X38),X39)),X106) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X38),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X39),X106)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_image__compose) ).

fof(fact_156_dense__le__bounded,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ( ! [X47] :
                ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X47))
               => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X35))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X36)) ) )
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_dense__le__bounded) ).

fof(fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X49,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_876_sup__inf__distrib2,axiom,
    ! [X1] :
      ( distrib_lattice(X1)
     => ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X36),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_sup__inf__distrib2) ).

fof(fact_877_inf__sup__distrib2,axiom,
    ! [X1] :
      ( distrib_lattice(X1)
     => ! [X35,X36,X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)),X34) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X36),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_inf__sup__distrib2) ).

fof(fact_616_comm__semiring__class_Odistrib,axiom,
    ! [X1] :
      ( comm_semiring(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_comm__semiring__class_Odistrib) ).

fof(fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X37)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_664_nat__0__less__mult__iff,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)))
    <=> ( 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)),X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_nat__0__less__mult__iff) ).

fof(fact_15_split__paired__All,axiom,
    ! [X1,X2,X11] :
      ( ! [X18] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,X18))
    <=> ! [X19,X20] : hBOOL(hAPP(product_prod(X1,X2),bool,X11,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X19),X20))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

fof(fact_507_inj__imp__surj__inv,axiom,
    ! [X1,X2,X38] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),top_top(fun(X1,bool))))
     => 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))),X38)),top_top(fun(X2,bool))) = top_top(fun(X1,bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_inj__imp__surj__inv) ).

fof(fact_802_UnI1,axiom,
    ! [X1,X43,X17,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_UnI1) ).

fof(fact_803_UnI2,axiom,
    ! [X1,X40,X17,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_UnI2) ).

fof(fact_797_Un__assoc,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_Un__assoc) ).

fof(fact_902_Int__assoc,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)),X52) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_Int__assoc) ).

fof(fact_604_add__mult__distrib,axiom,
    ! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X50)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_add__mult__distrib) ).

fof(fact_543_Ints__odd__nonzero,axiom,
    ! [X1] :
      ( ring_char_0(X1)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),ring_1_Ints(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)),X14)),X14) != zero_zero(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_Ints__odd__nonzero) ).

fof(fact_346_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( 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),X14),X14)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_351_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X1] :
      ( linord219039673up_add(X1)
     => ! [X14] :
          ( 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),X14),X14)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_201_rev__predicate2D,axiom,
    ! [X2,X1,X53,X11,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
     => ( 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))),X11),X53))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_rev__predicate2D) ).

fof(fact_203_predicate2D,axiom,
    ! [X1,X2,X6,X7,X11,X53] :
      ( 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))),X11),X53))
     => ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X11,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X53,X6),X7)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_predicate2D) ).

fof(fact_282_card__mono,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_card__mono) ).

fof(fact_280_psubset__card__mono,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_psubset__card__mono) ).

fof(fact_790_finite__Un,axiom,
    ! [X1,X25,X112] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112)))
    <=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_finite__Un) ).

fof(fact_413_less__add__Suc1,axiom,
    ! [X58,X49] : 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),X49)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_less__add__Suc1) ).

fof(fact_414_less__add__Suc2,axiom,
    ! [X58,X49] : 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),X49),X58)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_less__add__Suc2) ).

fof(fact_204_subset__trans,axiom,
    ! [X1,X52,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X52)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_subset__trans) ).

fof(fact_199_psubset__subset__trans,axiom,
    ! [X1,X52,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X52))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_psubset__subset__trans) ).

fof(fact_200_subset__psubset__trans,axiom,
    ! [X1,X52,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_subset__psubset__trans) ).

fof(fact_266_psubset__trans,axiom,
    ! [X1,X52,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X43),X52))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X52)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_psubset__trans) ).

fof(fact_899_inf1D1,axiom,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
     => hBOOL(hAPP(X1,bool,X40,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_inf1D1) ).

fof(fact_898_inf1D2,axiom,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
     => hBOOL(hAPP(X1,bool,X43,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_inf1D2) ).

fof(fact_403_Suc__le__mono,axiom,
    ! [X30,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),hAPP(nat,nat,suc,X54)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Suc__le__mono) ).

fof(fact_394_Suc__less__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_Suc__less__eq) ).

fof(fact_386_Suc__less__SucD,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_Suc__less__SucD) ).

fof(fact_464_rangeI,axiom,
    ! [X1,X2,X38,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X38,X6)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),top_top(fun(X2,bool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_rangeI) ).

fof(fact_163_subset__inj__on,axiom,
    ! [X1,X2,X40,X38,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_subset__inj__on) ).

fof(fact_389_less__trans__Suc,axiom,
    ! [X50,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),X50))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_less__trans__Suc) ).

fof(fact_750_folding__idem_Oidem__comp,axiom,
    ! [X1,X2,X6,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X38),X25))
     => hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(X1,fun(X2,X2),X38,X6)),hAPP(X1,fun(X2,X2),X38,X6)) = hAPP(X1,fun(X2,X2),X38,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_folding__idem_Oidem__comp) ).

fof(fact_854_ivl__disj__un_I12_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X77,X66] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X77),X66))
         => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_ivl__disj__un_I12_J) ).

fof(fact_812_ivl__disj__un_I11_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X77,X66] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
         => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X77) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_ivl__disj__un_I11_J) ).

fof(fact_865_ivl__disj__un_I14_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X77,X66] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
         => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_ivl__disj__un_I14_J) ).

fof(fact_855_ivl__disj__un_I13_J,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X77,X66] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X77),X66))
         => hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X77),X66)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X66)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X77) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_ivl__disj__un_I13_J) ).

fof(fact_735_comp__cong,axiom,
    ! [X2,X1,X3,X87,X109,X38,X39,X6,X105,X110,X111] :
      ( hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)) = hAPP(X87,X1,X105,hAPP(X109,X87,X110,X111))
     => hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X109,X1,hAPP(fun(X109,X87),fun(X109,X1),hAPP(fun(X87,X1),fun(fun(X109,X87),fun(X109,X1)),comp(X87,X1,X109),X105),X110),X111) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_comp__cong) ).

fof(fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_878_sup__inf__distrib1,axiom,
    ! [X1] :
      ( distrib_lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_sup__inf__distrib1) ).

fof(fact_879_inf__sup__distrib1,axiom,
    ! [X1] :
      ( distrib_lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_inf__sup__distrib1) ).

fof(fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X35)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X95) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_933_inf__sup__ord_I1_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_inf__sup__ord_I1_J) ).

fof(fact_932_inf__le1,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_inf__le1) ).

fof(fact_931_inf__sup__ord_I2_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_inf__sup__ord_I2_J) ).

fof(fact_930_inf__le2,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_inf__le2) ).

fof(fact_310_finite__Plus,axiom,
    ! [X2,X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
       => 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),X40),X43))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_finite__Plus) ).

fof(fact_206_set__rev__mp,axiom,
    ! [X1,X43,X6,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_set__rev__mp) ).

fof(fact_208_in__mono,axiom,
    ! [X1,X6,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_in__mono) ).

fof(fact_205_set__mp,axiom,
    ! [X1,X6,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_set__mp) ).

fof(fact_195_subsetD,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subsetD) ).

fof(fact_265_psubsetD,axiom,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_psubsetD) ).

fof(fact_106_le__funD,axiom,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X6,X38,X39] :
          ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
         => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_le__funD) ).

fof(fact_96_le__funE,axiom,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X6,X38,X39] :
          ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
         => hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,X2,X39,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__funE) ).

fof(fact_959_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X57,X38] :
          ( hAPP(nat,X1,X38,zero_zero(nat)) = zero_zero(X1)
         => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_956_setsum__shift__lb__Suc0__0,axiom,
    ! [X57,X38] :
      ( hAPP(nat,nat,X38,zero_zero(nat)) = zero_zero(nat)
     => hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X57)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_setsum__shift__lb__Suc0__0) ).

fof(fact_605_add__mult__distrib2,axiom,
    ! [X50,X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X49)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X50),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_add__mult__distrib2) ).

fof(fact_842_le__supI1,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X22,X34,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_le__supI1) ).

fof(fact_843_le__supI2,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X34,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_le__supI2) ).

fof(fact_851_less__supI1,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X22,X34,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X21))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_less__supI1) ).

fof(fact_850_less__supI2,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X34,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X22))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_less__supI2) ).

fof(fact_316_card__Plus__conv__if,axiom,
    ! [X2,X1,X43,X40] :
      ( ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
          & hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
       => hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) )
      & ( ~ ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
            & hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43)) )
       => hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(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),X40),X43)) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_card__Plus__conv__if) ).

fof(fact_305_card__Plus,axiom,
    ! [X2,X1,X43,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X43))
       => hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(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),X40),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X40)),hAPP(fun(X2,bool),nat,finite_card(X2),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_card__Plus) ).

fof(fact_499_eq__card__imp__inj__on,axiom,
    ! [X2,X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40)
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_eq__card__imp__inj__on) ).

fof(fact_500_inj__on__iff__eq__card,axiom,
    ! [X2,X1,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
      <=> 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_inj__on__iff__eq__card) ).

fof(fact_262_termination__basic__simps_I3_J,axiom,
    ! [X36,X34,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_termination__basic__simps_I3_J) ).

fof(fact_251_trans__le__add1,axiom,
    ! [X49,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),X49))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_trans__le__add1) ).

fof(fact_263_termination__basic__simps_I4_J,axiom,
    ! [X35,X34,X36] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X36))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_termination__basic__simps_I4_J) ).

fof(fact_252_trans__le__add2,axiom,
    ! [X49,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),X49),X59))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_trans__le__add2) ).

fof(fact_268_termination__basic__simps_I1_J,axiom,
    ! [X36,X34,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_termination__basic__simps_I1_J) ).

fof(fact_236_trans__less__add1,axiom,
    ! [X49,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),X49))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_trans__less__add1) ).

fof(fact_267_termination__basic__simps_I2_J,axiom,
    ! [X35,X34,X36] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X36))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_termination__basic__simps_I2_J) ).

fof(fact_237_trans__less__add2,axiom,
    ! [X49,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),X49),X59))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_trans__less__add2) ).

fof(fact_440_Suc__lessE,axiom,
    ! [X58,X50] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X50))
     => ~ ! [X64] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
           => X50 != hAPP(nat,nat,suc,X64) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_Suc__lessE) ).

fof(fact_400_Suc__leD,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_Suc__leD) ).

fof(fact_422_Suc__le__lessD,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_Suc__le__lessD) ).

fof(fact_418_Suc__le__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_Suc__le__eq) ).

fof(fact_416_less__eq__Suc__le,axiom,
    ! [X30,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_less__eq__Suc__le) ).

fof(fact_387_Suc__lessD,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_Suc__lessD) ).

fof(fact_795_Un__left__commute,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_Un__left__commute) ).

fof(fact_904_Int__left__commute,axiom,
    ! [X1,X40,X43,X52] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X52)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X52)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_Int__left__commute) ).

fof(fact_789_finite__UnI,axiom,
    ! [X1,X112,X25] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112))
       => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X25),X112))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_finite__UnI) ).

fof(fact_374_Suc__mono,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),hAPP(nat,nat,suc,X51))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_Suc__mono) ).

fof(fact_712_ex__has__least__nat,axiom,
    ! [X1,X54,X11,X57] :
      ( hBOOL(hAPP(X1,bool,X11,X57))
     => ? [X26] :
          ( hBOOL(hAPP(X1,bool,X11,X26))
          & ! [X46] :
              ( hBOOL(hAPP(X1,bool,X11,X46))
             => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X54,X26)),hAPP(X1,nat,X54,X46))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_ex__has__least__nat) ).

fof(fact_550_image__restrict__eq,axiom,
    ! [X2,X1,X38,X40] : hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(X2,X1),X38),X40)),X40) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_image__restrict__eq) ).

fof(fact_716_Collect__mono,axiom,
    ! [X1,X53,X11] :
      ( ! [X26] :
          ( hBOOL(hAPP(X1,bool,X11,X26))
         => hBOOL(hAPP(X1,bool,X53,X26)) )
     => 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),collect(X1),X11)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X53))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_Collect__mono) ).

fof(fact_782_Un__upper1,axiom,
    ! [X1,X40,X43] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_Un__upper1) ).

fof(fact_783_Un__upper2,axiom,
    ! [X1,X43,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_Un__upper2) ).

fof(fact_871_inf1I,axiom,
    ! [X1,X43,X40,X6] :
      ( hBOOL(hAPP(X1,bool,X40,X6))
     => ( hBOOL(hAPP(X1,bool,X43,X6))
       => hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_inf1I) ).

fof(fact_99_order__trans,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_order__trans) ).

fof(fact_97_xt1_I6_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X36,X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_xt1_I6_J) ).

fof(fact_128_order__less__le__trans,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__less__le__trans) ).

fof(fact_130_order__le__less__trans,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__le__less__trans) ).

fof(fact_56_order__less__trans,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X36,X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X36))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X36)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_order__less__trans) ).

fof(fact_129_xt1_I7_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X36,X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X36),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_xt1_I7_J) ).

fof(fact_131_xt1_I8_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X36,X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_xt1_I8_J) ).

fof(fact_55_xt1_I10_J,axiom,
    ! [X1] :
      ( order(X1)
     => ! [X36,X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X36),X34)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_xt1_I10_J) ).

fof(fact_230_le__trans,axiom,
    ! [X50,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),X50))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_le__trans) ).

fof(fact_240_less__add__eq__less,axiom,
    ! [X49,X51,X50,X61] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X50),X61))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X50),X51)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_less__add__eq__less) ).

fof(fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X49,X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X49)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1))),X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_834_inf__sup__aci_I6_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_inf__sup__aci_I6_J) ).

fof(fact_835_sup__assoc,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_sup__assoc) ).

fof(fact_833_sup_Oassoc,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_sup_Oassoc) ).

fof(fact_939_inf__sup__aci_I2_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_inf__sup__aci_I2_J) ).

fof(fact_940_inf_Oassoc,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_inf_Oassoc) ).

fof(fact_938_inf__assoc,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)),X36) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_inf__assoc) ).

fof(fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X95,X93] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X95)),X93) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X95),X93)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_599_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X1] :
      ( ab_semigroup_mult(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_170_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X1] :
      ( ab_semigroup_add(X1)
     => ! [X21,X22,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X22)),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X93)),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37)),X45) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_421_le__less__Suc__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
      <=> X30 = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_le__less__Suc__eq) ).

fof(fact_703_nat__mult__assoc,axiom,
    ! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_nat__mult__assoc) ).

fof(fact_224_nat__add__assoc,axiom,
    ! [X49,X51,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),X50) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_nat__add__assoc) ).

fof(fact_860_atLeast__iff,axiom,
    ! [X1] :
      ( ord(X1)
     => ! [X29,X57] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X57)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X57),X29)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_atLeast__iff) ).

fof(fact_538_greaterThan__iff,axiom,
    ! [X1] :
      ( ord(X1)
     => ! [X29,X57] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X29),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X57)))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X57),X29)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_greaterThan__iff) ).

fof(fact_390_Suc__lessI,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => ( hAPP(nat,nat,suc,X49) != X51
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X49)),X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_Suc__lessI) ).

fof(fact_872_finite__Int,axiom,
    ! [X1,X112,X25] :
      ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
        | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X112)) )
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X25),X112))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_finite__Int) ).

fof(fact_483_card__image,axiom,
    ! [X1,X2,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X38),X40))
     => 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),X38),X40)) = hAPP(fun(X1,bool),nat,finite_card(X1),X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_card__image) ).

fof(fact_420_Suc__leI,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X49)),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_Suc__leI) ).

fof(fact_800_sup1I1,axiom,
    ! [X1,X43,X40,X6] :
      ( hBOOL(hAPP(X1,bool,X40,X6))
     => hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_sup1I1) ).

fof(fact_801_sup1I2,axiom,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,X43,X6))
     => hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_sup1I2) ).

fof(fact_425_card__Collect__le__nat,axiom,
    ! [X30] : 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)),X30))) = hAPP(nat,nat,suc,X30),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_card__Collect__le__nat) ).

fof(fact_459_finite__imageI,axiom,
    ! [X2,X1,X76,X25] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
     => 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),X76),X25))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_finite__imageI) ).

fof(fact_404_le__Suc__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X30)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
        | X54 = hAPP(nat,nat,suc,X30) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_le__Suc__eq) ).

fof(fact_438_Suc__le__D,axiom,
    ! [X51,X73] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X73))
     => ? [X33] : X73 = hAPP(nat,nat,suc,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_Suc__le__D) ).

fof(fact_430_inc__induct,axiom,
    ! [X11,X29,X63] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),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,X29)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_inc__induct) ).

fof(fact_291_card__Collect__less__nat,axiom,
    ! [X30] : 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)),X30))) = X30,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_card__Collect__less__nat) ).

fof(fact_410_less__Suc__eq__0__disj,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
    <=> ( X54 = zero_zero(nat)
        | ? [X64] :
            ( X54 = hAPP(nat,nat,suc,X64)
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X30)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_less__Suc__eq__0__disj) ).

fof(fact_259_subsetI,axiom,
    ! [X1,X43,X40] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X43)) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_subsetI) ).

fof(fact_732_o__eq__elim,axiom,
    ! [X1,X3,X2,X87,X14,X15,X17,X81] :
      ( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
     => ! [X108] : hAPP(X3,X2,X14,hAPP(X1,X3,X15,X108)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X108)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_o__eq__elim) ).

fof(fact_731_o__eq__dest,axiom,
    ! [X1,X3,X2,X87,X107,X14,X15,X17,X81] :
      ( hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X14),X15) = hAPP(fun(X1,X87),fun(X1,X2),hAPP(fun(X87,X2),fun(fun(X1,X87),fun(X1,X2)),comp(X87,X2,X1),X17),X81)
     => hAPP(X3,X2,X14,hAPP(X1,X3,X15,X107)) = hAPP(X87,X2,X17,hAPP(X1,X87,X81,X107)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_o__eq__dest) ).

fof(fact_495_finite__UNIV__inj__surj,axiom,
    ! [X1,X38] :
      ( 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),X38),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),X38),top_top(fun(X1,bool))) = top_top(fun(X1,bool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_finite__UNIV__inj__surj) ).

fof(fact_986_setsum__eq__0__iff,axiom,
    ! [X1,X38,X25] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X25))
     => ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X38),X25) = zero_zero(nat)
      <=> ! [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X25))
           => hAPP(X1,nat,X38,X26) = zero_zero(nat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_setsum__eq__0__iff) ).

fof(fact_395_less__Suc__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
        | X54 = X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_less__Suc__eq) ).

fof(fact_417_less__Suc__eq__le,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X30)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_less__Suc__eq__le) ).

fof(fact_606_Suc__mult__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X57)),X30)
    <=> X54 = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_Suc__mult__cancel1) ).

fof(fact_198_psubset__imp__subset,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X40),X43))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_psubset__imp__subset) ).

fof(fact_303_finite__nat__set__iff__bounded__le,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X33] :
        ! [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),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_finite__nat__set__iff__bounded__le) ).

fof(fact_304_finite__nat__set__iff__bounded,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X33] :
        ! [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),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_finite__nat__set__iff__bounded) ).

fof(fact_515_image__Suc__atLeastLessThan,axiom,
    ! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_image__Suc__atLeastLessThan) ).

fof(fact_766_image__Suc__atLeastAtMost,axiom,
    ! [X29,X63] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X29),X63)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X63)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_image__Suc__atLeastAtMost) ).

fof(fact_496_finite__UNIV__surj__inj,axiom,
    ! [X1,X38] :
      ( 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),X38),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X38),top_top(fun(X1,bool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_finite__UNIV__surj__inj) ).

fof(fact_63_order__less__imp__triv,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X11,X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
           => hBOOL(X11) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_order__less__imp__triv) ).

fof(fact_402_le__SucI,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_le__SucI) ).

fof(fact_419_le__imp__less__Suc,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_le__imp__less__Suc) ).

fof(fact_391_less__SucI,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_less__SucI) ).

fof(fact_817_sup__fun__def,axiom,
    ! [X1,X2] :
      ( lattice(X2)
     => ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_sup_sup(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_sup_sup(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_sup__fun__def) ).

fof(fact_816_sup__apply,axiom,
    ! [X2,X1] :
      ( lattice(X1)
     => ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_sup_sup(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_sup__apply) ).

fof(fact_950_inf__fun__def,axiom,
    ! [X1,X2] :
      ( lattice(X2)
     => ! [X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X2),fun(X1,X2)),semilattice_inf_inf(fun(X1,X2)),X38),X39),X26) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),semilattice_inf_inf(X2),hAPP(X1,X2,X38,X26)),hAPP(X1,X2,X39,X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_inf__fun__def) ).

fof(fact_937_inf__apply,axiom,
    ! [X2,X1] :
      ( lattice(X1)
     => ! [X38,X39,X6] : hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_inf_inf(fun(X2,X1)),X38),X39),X6) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X2,X1,X38,X6)),hAPP(X2,X1,X39,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_inf__apply) ).

fof(fact_706_nat__mult__eq__cancel1,axiom,
    ! [X54,X30,X57] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
      <=> X54 = X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_nat__mult__eq__cancel1) ).

fof(fact_364_zero__less__two,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => 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)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_zero__less__two) ).

fof(fact_231_le__antisym,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49))
       => X49 = X51 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_le__antisym) ).

fof(fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X49] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X49),X49) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_619_zero__le__square,axiom,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_zero__le__square) ).

fof(fact_151_less__add__one,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),one_one(X1)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__add__one) ).

fof(fact_831_inf__sup__aci_I7_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_inf__sup__aci_I7_J) ).

fof(fact_832_sup__left__commute,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_sup__left__commute) ).

fof(fact_830_sup_Oleft__commute,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_sup_Oleft__commute) ).

fof(fact_942_inf__sup__aci_I3_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_inf__sup__aci_I3_J) ).

fof(fact_943_inf_Oleft__commute,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X22,X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X37)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_inf_Oleft__commute) ).

fof(fact_941_inf__left__commute,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35,X36] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X36)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_inf__left__commute) ).

fof(fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X92,X93,X94] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),X94)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X93),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X92),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X37,X45] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X45)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_836_inf__sup__ord_I3_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_inf__sup__ord_I3_J) ).

fof(fact_837_sup__ge1,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_sup__ge1) ).

fof(fact_838_inf__sup__ord_I4_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_inf__sup__ord_I4_J) ).

fof(fact_839_sup__ge2,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X35,X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_sup__ge2) ).

fof(fact_155_dense__le,axiom,
    ! [X1] :
      ( dense_linorder(X1)
     => ! [X36,X35] :
          ( ! [X26] :
              ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X35))
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X36)) )
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X36)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dense__le) ).

fof(fact_524_finite__imp__inj__to__nat__seg,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ? [X84,X44] :
          ( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),X84),X40) = 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)),X44))
          & hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),X84),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_finite__imp__inj__to__nat__seg) ).

fof(fact_365_card__ge__0__finite,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X40)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_card__ge__0__finite) ).

fof(fact_293_finite__subset,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_finite__subset) ).

fof(fact_292_rev__finite__subset,axiom,
    ! [X1,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_rev__finite__subset) ).

fof(fact_794_Un__left__absorb,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_Un__left__absorb) ).

fof(fact_905_Int__left__absorb,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_Int__left__absorb) ).

fof(fact_572_le__square,axiom,
    ! [X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X49))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_le__square) ).

fof(fact_248_le__add1,axiom,
    ! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_le__add1) ).

fof(fact_247_le__add2,axiom,
    ! [X51,X49] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_le__add2) ).

fof(fact_221_nat__less__cases,axiom,
    ! [X11,X54,X30] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
     => ( ( X54 = X30
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X30),X54)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_nat__less__cases) ).

fof(fact_223_nat__add__left__commute,axiom,
    ! [X34,X35,X36] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X36)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X36)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_nat__add__left__commute) ).

fof(fact_207_predicate1D,axiom,
    ! [X1,X6,X11,X53] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
     => ( hBOOL(hAPP(X1,bool,X11,X6))
       => hBOOL(hAPP(X1,bool,X53,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_predicate1D) ).

fof(fact_211_rev__predicate1D,axiom,
    ! [X1,X53,X11,X6] :
      ( hBOOL(hAPP(X1,bool,X11,X6))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53))
       => hBOOL(hAPP(X1,bool,X53,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_rev__predicate1D) ).

fof(fact_415_less__iff__Suc__add,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
    <=> ? [X62] : X30 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_less__iff__Suc__add) ).

fof(help_COMBS_1_1_U,axiom,
    ! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3)),combs(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),hAPP(X1,X2,X119,X120)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

fof(fact_439_lessE,axiom,
    ! [X58,X50] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X50))
     => ( X50 != hAPP(nat,nat,suc,X58)
       => ~ ! [X64] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
             => X50 != hAPP(nat,nat,suc,X64) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_lessE) ).

fof(fact_431_less__imp__Suc__add,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => ? [X62] : X51 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X62)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_less__imp__Suc__add) ).

fof(fact_123_order__less__imp__le,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_order__less__imp__le) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res) ).

fof(fact_667_mult__Suc,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_mult__Suc) ).

fof(fact_549_finite__greaterThanLessThan,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_gr676655987ssThan(nat),X77),X66))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_finite__greaterThanLessThan) ).

fof(fact_548_finite__greaterThanAtMost,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_gr1471790799AtMost(nat),X77),X66))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_finite__greaterThanAtMost) ).

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/sandbox/benchmark/theBenchmark.p',fact_460_finite__atLeastLessThan) ).

fof(fact_761_finite__atLeastAtMost,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_atLeastAtMost(nat),X77),X66))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_finite__atLeastAtMost) ).

fof(fact_370_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/sandbox/benchmark/theBenchmark.p',fact_370_less__imp__add__positive) ).

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

fof(fact_245_le__neq__implies__less,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
     => ( X49 != X51
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_le__neq__implies__less) ).

fof(fact_243_le__eq__less__or__eq,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
        | X54 = X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_le__eq__less__or__eq) ).

fof(fact_242_nat__less__le,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
        & X54 != X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__less__le) ).

fof(fact_264_termination__basic__simps_I5_J,axiom,
    ! [X34,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_termination__basic__simps_I5_J) ).

fof(fact_246_less__or__eq__imp__le,axiom,
    ! [X49,X51] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
        | X49 = X51 )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_less__or__eq__imp__le) ).

fof(fact_244_less__imp__le__nat,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_less__imp__le__nat) ).

fof(fact_409_less__Suc0,axiom,
    ! [X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> X30 = zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_less__Suc0) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res,axiom,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res) ).

fof(fact_366_finite__UNIV__card__ge__0,axiom,
    ! [X1] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
     => 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))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_finite__UNIV__card__ge__0) ).

fof(fact_271_linear__alt,axiom,
    ? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X65),arrow_1568854078le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_linear__alt) ).

fof(fact_444_nat__induct,axiom,
    ! [X30,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,X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_nat__induct) ).

fof(fact_730_o__apply,axiom,
    ! [X3,X1,X2,X38,X39,X6] : hAPP(X3,X1,hAPP(fun(X3,X2),fun(X3,X1),hAPP(fun(X2,X1),fun(fun(X3,X2),fun(X3,X1)),comp(X2,X1,X3),X38),X39),X6) = hAPP(X2,X1,X38,hAPP(X3,X2,X39,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_o__apply) ).

fof(fact_728_o__def,axiom,
    ! [X1,X2,X3,X38,X39,X26] : hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X38),X39),X26) = hAPP(X3,X2,X38,hAPP(X1,X3,X39,X26)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_o__def) ).

fof(help_COMBB_1_1_U,axiom,
    ! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X118),X119),X120) = hAPP(X2,X3,X118,hAPP(X1,X2,X119,X120)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

fof(help_COMBC_1_1_U,axiom,
    ! [X1,X3,X2,X118,X119,X120] : hAPP(X1,X3,hAPP(X2,fun(X1,X3),hAPP(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3)),combc(X1,X2,X3),X118),X119),X120) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X118,X120),X119),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

fof(fact_666_mult__Suc__right,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_mult__Suc__right) ).

fof(fact_398_add__Suc,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_add__Suc) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res) ).

fof(fact_76_mem__def,axiom,
    ! [X1,X6,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40))
    <=> hBOOL(hAPP(X1,bool,X40,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).

fof(fact_249_le__iff__add,axiom,
    ! [X54,X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
    <=> ? [X62] : X30 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_le__iff__add) ).

fof(fact_828_inf__sup__aci_I8_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_inf__sup__aci_I8_J) ).

fof(fact_829_sup__left__idem,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_sup__left__idem) ).

fof(fact_827_sup_Oleft__idem,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_sup_Oleft__idem) ).

fof(fact_945_inf__sup__aci_I4_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_inf__sup__aci_I4_J) ).

fof(fact_946_inf_Oleft__idem,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_inf_Oleft__idem) ).

fof(fact_944_inf__left__idem,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_inf__left__idem) ).

fof(fact_821_mult__left__idem,axiom,
    ! [X1] :
      ( ab_sem1668676832m_mult(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_mult__left__idem) ).

fof(fact_717_predicate1I,axiom,
    ! [X1,X53,X11] :
      ( ! [X26] :
          ( hBOOL(hAPP(X1,bool,X11,X26))
         => hBOOL(hAPP(X1,bool,X53,X26)) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X11),X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_predicate1I) ).

fof(fact_109_linorder__linear,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
          | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_linorder__linear) ).

fof(fact_113_linorder__le__less__linear,axiom,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
          | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_linorder__le__less__linear) ).

fof(fact_315_bounded__nat__set__is__finite,axiom,
    ! [X30,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),X30)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_bounded__nat__set__is__finite) ).

fof(fact_295_finite__Plus__UNIV__iff,axiom,
    ! [X1,X2] :
      ( 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)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_finite__Plus__UNIV__iff) ).

fof(fact_296_finite__Prod__UNIV,axiom,
    ! [X2,X1] :
      ( 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))))
       => hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_finite__Prod__UNIV) ).

fof(fact_216_nat__neq__iff,axiom,
    ! [X54,X30] :
      ( X54 != X30
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_nat__neq__iff) ).

fof(fact_228_nat__le__linear,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X49)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__le__linear) ).

fof(fact_368_card_Oneutral,axiom,
    ! [X1,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( ( ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_card_Oneutral) ).

fof(fact_399_add__Suc__right,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_add__Suc__right) ).

fof(fact_540_nat__case__Suc,axiom,
    ! [X1,X28,X86,X67] : hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X28),X86),hAPP(nat,nat,suc,X67)) = hAPP(nat,X1,X86,X67),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_nat__case__Suc) ).

fof(fact_397_add__Suc__shift,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X49)),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),hAPP(nat,nat,suc,X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_add__Suc__shift) ).

fof(fact_740_nat_Osize_I4_J,axiom,
    ! [X104] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X104)),hAPP(nat,nat,suc,zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_nat_Osize_I4_J) ).

fof(fact_719_nat_Osize_I2_J,axiom,
    ! [X104] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X104)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X104)),hAPP(nat,nat,suc,zero_zero(nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_nat_Osize_I2_J) ).

fof(fact_372_finite__fun__UNIVD1,axiom,
    ! [X1,X2] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool))))
     => ( 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)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_finite__fun__UNIVD1) ).

fof(fact_443_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/sandbox/benchmark/theBenchmark.p',fact_443_zero__induct) ).

fof(fact_554_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X77),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_767_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X77)),X66) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X77),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_432_gr0__implies__Suc,axiom,
    ! [X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51))
     => ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_gr0__implies__Suc) ).

fof(fact_408_gr0__conv__Suc,axiom,
    ! [X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30))
    <=> ? [X33] : X30 = hAPP(nat,nat,suc,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_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_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))))
       => hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),X78),top_top(fun(arrow_1998540521e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))) ),
    file('/export/starexec/sandbox/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_89_Pi__UNIV,axiom,
    ! [X1,X2,X40] : 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),X40),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)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Pi__UNIV) ).

fof(fact_375_zero__less__Suc,axiom,
    ! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X51))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_zero__less__Suc) ).

fof(fact_373_lessI,axiom,
    ! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X51))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_lessI) ).

fof(fact_330_neq0__conv,axiom,
    ! [X30] :
      ( X30 != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_neq0__conv) ).

fof(fact_338_le__0__eq,axiom,
    ! [X30] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),zero_zero(nat)))
    <=> X30 = zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_le__0__eq) ).

fof(fact_332_gr__implies__not0,axiom,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
     => X51 != zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_gr__implies__not0) ).

fof(fact_220_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/sandbox/benchmark/theBenchmark.p',fact_220_less__not__refl3) ).

fof(fact_219_less__not__refl2,axiom,
    ! [X51,X49] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
     => X49 != X51 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_less__not__refl2) ).

fof(fact_607_mult__cancel2,axiom,
    ! [X54,X57,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X30),X57)
    <=> ( X54 = X30
        | X57 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_mult__cancel2) ).

fof(fact_707_nat__mult__eq__cancel__disj,axiom,
    ! [X57,X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
    <=> ( X57 = zero_zero(nat)
        | X54 = X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_nat__mult__eq__cancel__disj) ).

fof(fact_608_mult__cancel1,axiom,
    ! [X57,X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X57),X30)
    <=> ( X54 = X30
        | X57 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_mult__cancel1) ).

fof(fact_226_nat__add__right__cancel,axiom,
    ! [X54,X57,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X30),X57)
    <=> X54 = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_nat__add__right__cancel) ).

fof(fact_225_nat__add__left__cancel,axiom,
    ! [X57,X54,X30] :
      ( 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),X30)
    <=> X54 = X30 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_nat__add__left__cancel) ).

fof(fact_990_card__eq__setsum,axiom,
    ! [X1,X40] : hAPP(fun(X1,bool),nat,finite_card(X1),X40) = hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_card__eq__setsum) ).

fof(fact_793_Un__commute,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X43),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_Un__commute) ).

fof(fact_906_Int__commute,axiom,
    ! [X1,X40,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X43),X40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_Int__commute) ).

fof(fact_300_finite__fun__UNIVD2,axiom,
    ! [X1,X2] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool))))
     => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_finite__fun__UNIVD2) ).

fof(fact_763_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X77,X66] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),hAPP(nat,nat,suc,X66)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X77),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_979_setsum__0,axiom,
    ! [X2,X1] :
      ( comm_monoid_add(X1)
     => ! [X40] : hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),combk(X1,X2),zero_zero(X1))),X40) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_setsum__0) ).

fof(fact_162_subset__UNIV,axiom,
    ! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),top_top(fun(X1,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_subset__UNIV) ).

fof(fact_411_add__is__1,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X30 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_add__is__1) ).

fof(fact_412_one__is__add,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30)
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X30 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_one__is__add) ).

fof(fact_213_subset__refl,axiom,
    ! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__refl) ).

fof(tsy_v_F_res,hypothesis,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_F_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res) ).

fof(fact_142_inj__on__id2,axiom,
    ! [X1,X40] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X40)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_inj__on__id2) ).

fof(fact_714_UNIV__witness,axiom,
    ! [X1] :
    ? [X26] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),top_top(fun(X1,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_UNIV__witness) ).

fof(fact_27_iso__tuple__UNIV__I,axiom,
    ! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_iso__tuple__UNIV__I) ).

fof(fact_26_UNIV__I,axiom,
    ! [X1,X6] : hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),top_top(fun(X1,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_UNIV__I) ).

fof(fact_407_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/sandbox/benchmark/theBenchmark.p',fact_407_inj__Suc) ).

fof(fact_535_Ints__0,axiom,
    ! [X1] :
      ( ring_1(X1)
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_Ints__0) ).

fof(fact_537_Ints__1,axiom,
    ! [X1] :
      ( ring_1(X1)
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_Ints__1) ).

fof(fact_659_mult__eq__1__iff,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
        & X30 = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_mult__eq__1__iff) ).

fof(fact_294_finite__option__UNIV,axiom,
    ! [X1] :
      ( 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)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_finite__option__UNIV) ).

fof(fact_352_zero__le__one,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_zero__le__one) ).

fof(fact_354_zero__less__one,axiom,
    ! [X1] :
      ( linordered_semidom(X1)
     => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_zero__less__one) ).

fof(fact_825_inf__sup__aci_I5_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_inf__sup__aci_I5_J) ).

fof(fact_826_sup__commute,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X35),X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_sup__commute) ).

fof(fact_824_sup_Ocommute,axiom,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X22),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_sup_Ocommute) ).

fof(fact_948_inf__sup__aci_I1_J,axiom,
    ! [X1] :
      ( lattice(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_inf__sup__aci_I1_J) ).

fof(fact_949_inf_Ocommute,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X22),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_inf_Ocommute) ).

fof(fact_947_inf__commute,axiom,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X35] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X34),X35) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X35),X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_inf__commute) ).

fof(fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X22] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X22) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X22),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21,X37] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X21),X37) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X37),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_132_top__greatest,axiom,
    ! [X1] :
      ( top(X1)
     => ! [X21] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),top_top(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_top__greatest) ).

fof(fact_313_UNIV__Plus__UNIV,axiom,
    ! [X2,X1] : 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),top_top(fun(X1,bool))),top_top(fun(X2,bool))) = top_top(fun(sum_sum(X1,X2),bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_UNIV__Plus__UNIV) ).

fof(fact_107_order__eq__refl,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( X34 = X35
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__eq__refl) ).

fof(fact_92_order__refl,axiom,
    ! [X1] :
      ( preorder(X1)
     => ! [X34] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_order__refl) ).

fof(fact_333_gr0I,axiom,
    ! [X51] :
      ( X51 != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_gr0I) ).

fof(fact_339_less__eq__nat_Osimps_I1_J,axiom,
    ! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_less__eq__nat_Osimps_I1_J) ).

fof(fact_320_le0,axiom,
    ! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_le0) ).

fof(fact_229_eq__imp__le,axiom,
    ! [X49,X51] :
      ( X49 = X51
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_eq__imp__le) ).

fof(fact_227_le__refl,axiom,
    ! [X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X51)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_le__refl) ).

fof(fact_702_nat__mult__commute,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_nat__mult__commute) ).

fof(fact_222_nat__add__commute,axiom,
    ! [X49,X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_nat__add__commute) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res,axiom,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res) ).

fof(fact_806_Un__UNIV__left,axiom,
    ! [X1,X43] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X43) = top_top(fun(X1,bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_Un__UNIV__left) ).

fof(fact_807_Un__UNIV__right,axiom,
    ! [X1,X40] : hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_Un__UNIV__right) ).

fof(fact_609_mult__is__0,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = zero_zero(nat)
    <=> ( X54 = zero_zero(nat)
        | X30 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_mult__is__0) ).

fof(fact_669_mult__eq__self__implies__10,axiom,
    ! [X49,X51] :
      ( X49 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),X51)
     => ( X51 = one_one(nat)
        | X49 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_mult__eq__self__implies__10) ).

fof(fact_336_add__is__0,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X30) = zero_zero(nat)
    <=> ( X54 = zero_zero(nat)
        & X30 = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_add__is__0) ).

fof(fact_600_nat__mult__eq__1__iff,axiom,
    ! [X54,X30] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30) = one_one(nat)
    <=> ( X54 = one_one(nat)
        & X30 = one_one(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_nat__mult__eq__1__iff) ).

fof(fact_602_nat__1__eq__mult__iff,axiom,
    ! [X54,X30] :
      ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X54),X30)
    <=> ( X54 = one_one(nat)
        & X30 = one_one(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_nat__1__eq__mult__iff) ).

fof(fact_337_add__eq__self__zero,axiom,
    ! [X49,X51] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X51) = X49
     => X51 = zero_zero(nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_add__eq__self__zero) ).

fof(fact_437_Suc__eq__plus1__left,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X51),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_Suc__eq__plus1__left) ).

fof(fact_436_Suc__eq__plus1,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),one_one(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_Suc__eq__plus1) ).

fof(fact_864_atLeast__Suc__greaterThan,axiom,
    ! [X57] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X57)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_atLeast__Suc__greaterThan) ).

fof(fact_424_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/sandbox/benchmark/theBenchmark.p',fact_424_less__eq__Suc__le__raw) ).

fof(fact_286_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_infinite__UNIV__nat) ).

fof(fact_78_UNIV__def,axiom,
    ! [X1] : top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_UNIV__def) ).

fof(tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res,axiom,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res) ).

fof(tsy_v_P_____res,hypothesis,
    ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),p) = p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_____res) ).

fof(fact_852_sup__top__left,axiom,
    ! [X1] :
      ( bounded_lattice_top(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X34) = top_top(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_sup__top__left) ).

fof(fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_598_mult__zero__left,axiom,
    ! [X1] :
      ( mult_zero(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X21) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_mult__zero__left) ).

fof(fact_853_sup__top__right,axiom,
    ! [X1] :
      ( bounded_lattice_top(X1)
     => ! [X34] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X34),top_top(X1)) = top_top(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_sup__top__right) ).

fof(fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X1] :
      ( comm_semiring_1(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_597_mult__zero__right,axiom,
    ! [X1] :
      ( mult_zero(X1)
     => ! [X21] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),zero_zero(X1)) = zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_mult__zero__right) ).

fof(fact_611_mult__0,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X51) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_mult__0) ).

fof(fact_603_nat__mult__1,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X51) = X51,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_nat__mult__1) ).

fof(fact_334_plus__nat_Oadd__0,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X51) = X51,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_plus__nat_Oadd__0) ).

fof(fact_610_mult__0__right,axiom,
    ! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X49),zero_zero(nat)) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_mult__0__right) ).

fof(fact_601_nat__mult__1__right,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X51),one_one(nat)) = X51,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_nat__mult__1__right) ).

fof(fact_335_Nat_Oadd__0__right,axiom,
    ! [X49] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),zero_zero(nat)) = X49,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Nat_Oadd__0__right) ).

fof(fact_377_nat_Oinject,axiom,
    ! [X67,X68] :
      ( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
    <=> X67 = X68 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_nat_Oinject) ).

fof(fact_376_Suc__inject,axiom,
    ! [X34,X35] :
      ( hAPP(nat,nat,suc,X34) = hAPP(nat,nat,suc,X35)
     => X34 = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_Suc__inject) ).

fof(fact_297_finite__UNIV,axiom,
    ! [X1] :
      ( finite_finite(X1)
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_finite__UNIV) ).

fof(fact_25_top1I,axiom,
    ! [X1,X6] : hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_top1I) ).

fof(fact_288_finite,axiom,
    ! [X1] :
      ( finite_finite(X1)
     => ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_finite) ).

fof(fact_287_finite__code,axiom,
    ! [X1] :
      ( finite_finite(X1)
     => ! [X40] : hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_finite__code) ).

fof(tsy_v_Lba_____res,axiom,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_Lba_____res) ).

fof(tsy_v_Lab_____res,axiom,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_Lab_____res) ).

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

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

fof(help_fNot_2_1_U,axiom,
    ! [X118] :
      ( hBOOL(X118)
      | hBOOL(hAPP(bool,bool,fNot,X118)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

fof(fact_383_Suc__not__Zero,axiom,
    ! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_Suc__not__Zero) ).

fof(fact_382_nat_Osimps_I3_J,axiom,
    ! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_nat_Osimps_I3_J) ).

fof(fact_380_Suc__neq__Zero,axiom,
    ! [X49] : hAPP(nat,nat,suc,X49) != zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_Suc__neq__Zero) ).

fof(fact_385_Zero__not__Suc,axiom,
    ! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_Zero__not__Suc) ).

fof(fact_384_nat_Osimps_I2_J,axiom,
    ! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_nat_Osimps_I2_J) ).

fof(fact_381_Zero__neq__Suc,axiom,
    ! [X49] : zero_zero(nat) != hAPP(nat,nat,suc,X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_Zero__neq__Suc) ).

fof(fact_378_Suc__n__not__n,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != X51,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_Suc__n__not__n) ).

fof(fact_379_n__not__Suc__n,axiom,
    ! [X51] : X51 != hAPP(nat,nat,suc,X51),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_n__not__Suc__n) ).

fof(tsy_c_Nat_Osize__class_Osize_res,axiom,
    ti(fun(nat,nat),size_size(nat)) = size_size(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Osize__class_Osize_res) ).

fof(tsy_c_Nat_Onat_Onat__size_res,axiom,
    ti(fun(nat,nat),nat_size) = nat_size,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Onat_Onat__size_res) ).

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

fof(tsy_c_HOL_Obool_Obool__size_res,axiom,
    ti(fun(bool,nat),bool_size) = bool_size,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Obool_Obool__size_res) ).

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

fof(tsy_v_h_____res,axiom,
    ti(fun(arrow_1998540521e_indi,nat),h) = h,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_h_____res) ).

fof(fact_29_top__apply,axiom,
    ! [X2,X1] :
      ( top(X1)
     => ! [X6] : hAPP(X2,X1,top_top(fun(X2,X1)),X6) = top_top(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top__apply) ).

fof(fact_442_nat_Oexhaust,axiom,
    ! [X35] :
      ( X35 != zero_zero(nat)
     => ~ ! [X74] : X35 != hAPP(nat,nat,suc,X74) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_nat_Oexhaust) ).

fof(fact_441_not0__implies__Suc,axiom,
    ! [X51] :
      ( X51 != zero_zero(nat)
     => ? [X33] : X51 = hAPP(nat,nat,suc,X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_not0__implies__Suc) ).

fof(fact_741_nat__size,axiom,
    ! [X51] : hAPP(nat,nat,size_size(nat),X51) = X51,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_nat__size) ).

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

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

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

fof(tsy_v_e_____res,axiom,
    ti(arrow_2142409994le_alt,e) = e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_e_____res) ).

fof(tsy_v_d_____res,hypothesis,
    ti(arrow_2142409994le_alt,d) = d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_d_____res) ).

fof(tsy_v_c_____res,hypothesis,
    ti(arrow_2142409994le_alt,c) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_c_____res) ).

fof(tsy_v_b_____res,axiom,
    ti(arrow_2142409994le_alt,b) = b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_b_____res) ).

fof(tsy_v_a_____res,axiom,
    ti(arrow_2142409994le_alt,a) = a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_a_____res) ).

fof(arity_sum___Finite__Set_Ofinite,axiom,
    ! [X114,X115] :
      ( ( finite_finite(X115)
        & finite_finite(X114) )
     => finite_finite(sum_sum(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).

fof(arity_fun___Finite__Set_Ofinite,axiom,
    ! [X114,X115] :
      ( ( finite_finite(X115)
        & finite_finite(X114) )
     => finite_finite(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).

fof(arity_prod___Finite__Set_Ofinite,axiom,
    ! [X114,X115] :
      ( ( finite_finite(X115)
        & finite_finite(X114) )
     => finite_finite(product_prod(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).

fof(arity_fun___Lattices_Obounded__lattice,axiom,
    ! [X114,X115] :
      ( bounded_lattice(X115)
     => bounded_lattice(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).

fof(arity_fun___Lattices_Odistrib__lattice,axiom,
    ! [X114,X115] :
      ( distrib_lattice(X115)
     => distrib_lattice(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Odistrib__lattice) ).

fof(arity_fun___Lattices_Obounded__lattice__top,axiom,
    ! [X114,X115] :
      ( bounded_lattice(X115)
     => bounded_lattice_top(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__top) ).

fof(arity_fun___Lattices_Olattice,axiom,
    ! [X114,X115] :
      ( lattice(X115)
     => lattice(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).

fof(arity_fun___Orderings_Opreorder,axiom,
    ! [X114,X115] :
      ( preorder(X115)
     => preorder(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).

fof(arity_fun___Orderings_Oorder,axiom,
    ! [X114,X115] :
      ( order(X115)
     => order(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).

fof(arity_fun___Orderings_Otop,axiom,
    ! [X114,X115] :
      ( top(X115)
     => top(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).

fof(arity_fun___Orderings_Oord,axiom,
    ! [X114,X115] :
      ( ord(X115)
     => ord(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).

fof(arity_fun___Lattices_Osemilattice__sup,axiom,
    ! [X114,X115] :
      ( lattice(X115)
     => semilattice_sup(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__sup) ).

fof(arity_fun___Lattices_Osemilattice__inf,axiom,
    ! [X114,X115] :
      ( lattice(X115)
     => semilattice_inf(fun(X114,X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).

fof(fact_328_one__neq__zero,axiom,
    ! [X1] :
      ( zero_neq_one(X1)
     => one_one(X1) != zero_zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_one__neq__zero) ).

fof(fact_327_zero__neq__one,axiom,
    ! [X1] :
      ( zero_neq_one(X1)
     => zero_zero(X1) != one_one(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_zero__neq__one) ).

fof(arity_Option_Ooption___Finite__Set_Ofinite,axiom,
    ! [X115] :
      ( finite_finite(X115)
     => finite_finite(option(X115)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option_Ooption___Finite__Set_Ofinite) ).

fof(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

fof(fact_82_n_I3_J,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_n_I3_J) ).

fof(fact_32_assms_I1_J,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
    file('/export/starexec/sandbox/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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_indi,bool))),h),n)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

fof(fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38__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_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

fof(fact_141_Prof__def,axiom,
    arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Prof__def) ).

fof(fact_36__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__096Lba_A_058_ALin_096) ).

fof(fact_35__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__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_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

fof(fact_457_surjh,axiom,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_surjh) ).

fof(fact_20_injh,axiom,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh) ).

fof(fact_531_greaterThan__0,axiom,
    hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_greaterThan__0) ).

fof(fact_1_u,axiom,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).

fof(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

fof(fact_276_finite__indi,axiom,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_finite__indi) ).

fof(fact_289_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/sandbox/benchmark/theBenchmark.p',fact_289_card__UNIV__unit) ).

fof(fact_863_atLeast__0,axiom,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_atLeast__0) ).

fof(fact_743_nat_Osize_I3_J,axiom,
    hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_nat_Osize_I3_J) ).

fof(fact_727_nat_Osize_I1_J,axiom,
    hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_nat_Osize_I1_J) ).

fof(fact_423_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_One__nat__def) ).

fof(fact_755_bool_Osize_I1_J,axiom,
    hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_bool_Osize_I1_J) ).

fof(fact_756_bool_Osize_I2_J,axiom,
    hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_bool_Osize_I2_J) ).

fof(arity_HOL_Obool___Lattices_Obounded__lattice,axiom,
    bounded_lattice(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).

fof(arity_Nat_Onat___Rings_Osemiring__0,axiom,
    semiring_0(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).

fof(arity_Nat_Onat___Lattices_Odistrib__lattice,axiom,
    distrib_lattice(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Odistrib__lattice) ).

fof(arity_HOL_Obool___Lattices_Odistrib__lattice,axiom,
    distrib_lattice(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Odistrib__lattice) ).

fof(arity_HOL_Obool___Lattices_Obounded__lattice__top,axiom,
    bounded_lattice_top(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__top) ).

fof(arity_Nat_Onat___Lattices_Olattice,axiom,
    lattice(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).

fof(arity_HOL_Obool___Lattices_Olattice,axiom,
    lattice(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).

fof(arity_Nat_Onat___Rings_Olinordered__semiring,axiom,
    linordered_semiring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).

fof(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
    linord893533164strict(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
    linord20386208strict(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).

fof(arity_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
    ordere1490568538miring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).

fof(arity_Nat_Onat___Rings_Oordered__semiring,axiom,
    ordered_semiring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).

fof(arity_Nat_Onat___Rings_Oordered__cancel__semiring,axiom,
    ordere453448008miring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).

fof(arity_Nat_Onat___Rings_Ocomm__semiring,axiom,
    comm_semiring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
    comm_monoid_mult(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(arity_Nat_Onat___Lattices_Osemilattice__sup,axiom,
    semilattice_sup(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__sup) ).

fof(arity_HOL_Obool___Lattices_Osemilattice__sup,axiom,
    semilattice_sup(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__sup) ).

fof(arity_Nat_Onat___Lattices_Osemilattice__inf,axiom,
    semilattice_inf(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).

fof(arity_HOL_Obool___Lattices_Osemilattice__inf,axiom,
    semilattice_inf(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).

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

fof(arity_Nat_Onat___Rings_Ono__zero__divisors,axiom,
    no_zero_divisors(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).

fof(arity_Nat_Onat___Rings_Omult__zero,axiom,
    mult_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).

fof(arity_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
    ab_semigroup_mult(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).

fof(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
    monoid_mult(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).

fof(arity_Nat_Onat___Rings_Osemiring,axiom,
    semiring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).

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

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

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

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

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

fof(fact_37__096a_A_126_061_Ab_096,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__096a_A_126_061_Ab_096) ).

fof(i_0_1167,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_45__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_1168,plain,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => ( ti(arrow_2142409994le_alt,X6) != ti(arrow_2142409994le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X7),X6)),X8)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_47_notin__Lin__iff]) ).

fof(i_0_1169,plain,
    ! [X1,X2,X15,X38,X40] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X40)))
     => ~ ! [X26] :
            ( ti(X1,X15) = hAPP(X2,X1,X38,X26)
           => ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X26),X40)) ) ),
    inference(fof_simplification,[status(thm)],[fact_512_imageE]) ).

fof(i_0_1170,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_124_linorder__antisym__conv2]) ).

fof(i_0_1171,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_70_linorder__antisym__conv3]) ).

fof(i_0_1172,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
          <=> ti(X1,X6) = ti(X1,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_119_linorder__antisym__conv1]) ).

fof(i_0_1173,plain,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X34,X35] :
          ( ti(X1,X34) != ti(X1,X35)
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_164_linorder__neqE__linordered__idom]) ).

fof(i_0_1174,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
            | ti(X1,X6) = ti(X1,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_72_not__less__iff__gr__or__eq]) ).

fof(i_0_1175,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ti(X1,X34) != ti(X1,X35)
         => ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_69_linorder__neqE]) ).

fof(i_0_1176,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ( ti(X1,X34) != ti(X1,X35)
           => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_53_linorder__cases]) ).

fof(i_0_1177,plain,
    ! [X1,X40,X43] :
      ( ti(fun(X1,bool),X40) = ti(fun(X1,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X40),X43))
         => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X40)) ) ),
    inference(fof_simplification,[status(thm)],[fact_202_equalityE]) ).

fof(i_0_1178,plain,
    ! [X1,X34,X35] :
      ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X34),X35))
      | ti(X1,X34) = ti(X1,X35) ),
    inference(fof_simplification,[status(thm)],[help_fequal_1_1_T]) ).

fof(i_0_1179,plain,
    ! [X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590] :
      ( ( hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590)),X6587))
        | hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6583),X6587) = hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6582),X6586)
        | hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590)),X6586))
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,finite_finite_1(X6580),X6587))
        | ~ hBOOL(hAPP(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool,hAPP(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool),hAPP(fun(X6581,fun(X6581,X6581)),fun(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool)),finite_folding_image(X6581,X6580),X6588),X6589),X6590)) )
      & ( ~ hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))),X6586))
        | hAPP(X6580,X6580,X6585,hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != ti(X6580,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | hAPP(X6580,X6581,X6582,hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != hAPP(X6580,X6581,X6583,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6583),X6587) = hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6582),X6586)
        | hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590)),X6586))
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,finite_finite_1(X6580),X6587))
        | ~ hBOOL(hAPP(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool,hAPP(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool),hAPP(fun(X6581,fun(X6581,X6581)),fun(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool)),finite_folding_image(X6581,X6580),X6588),X6589),X6590)) )
      & ( hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590)),X6587))
        | hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6583),X6587) = hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6582),X6586)
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),hAPP(X6580,X6580,X6585,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))),X6587))
        | hAPP(X6580,X6580,X6584,hAPP(X6580,X6580,X6585,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != ti(X6580,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,finite_finite_1(X6580),X6587))
        | ~ hBOOL(hAPP(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool,hAPP(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool),hAPP(fun(X6581,fun(X6581,X6581)),fun(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool)),finite_folding_image(X6581,X6580),X6588),X6589),X6590)) )
      & ( ~ hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))),X6586))
        | hAPP(X6580,X6580,X6585,hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != ti(X6580,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | hAPP(X6580,X6581,X6582,hAPP(X6580,X6580,X6584,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != hAPP(X6580,X6581,X6583,esk156_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6583),X6587) = hAPP(fun(X6580,bool),X6581,hAPP(fun(X6580,X6581),fun(fun(X6580,bool),X6581),X6590,X6582),X6586)
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,hAPP(X6580,fun(fun(X6580,bool),bool),member(X6580),hAPP(X6580,X6580,X6585,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))),X6587))
        | hAPP(X6580,X6580,X6584,hAPP(X6580,X6580,X6585,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))) != ti(X6580,esk155_11(X6580,X6581,X6582,X6583,X6584,X6585,X6586,X6587,X6588,X6589,X6590))
        | ~ hBOOL(hAPP(fun(X6580,bool),bool,finite_finite_1(X6580),X6587))
        | ~ hBOOL(hAPP(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool,hAPP(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool),hAPP(fun(X6581,fun(X6581,X6581)),fun(X6581,fun(fun(fun(X6580,X6581),fun(fun(X6580,bool),X6581)),bool)),finite_folding_image(X6581,X6580),X6588),X6589),X6590)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_757_folding__image_Oeq__general__inverses])])])]) ).

fof(i_0_1180,plain,
    ! [X7605,X7606] : hAPP(X7605,X7605,combi(X7605),X7606) = ti(X7605,X7606),
    inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).

fof(i_0_1181,plain,
    ! [X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338] :
      ( ( hBOOL(hAPP(fun(X6330,bool),bool,hAPP(X6330,fun(fun(X6330,bool),bool),member(X6330),esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338)),X6338))
        | hAPP(fun(X6330,bool),X6331,hAPP(X6331,fun(fun(X6330,bool),X6331),hAPP(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331))),finite_fold_image(X6331,X6330),times_times(X6331)),X6334),X6332),X6338) = hAPP(fun(X6329,bool),X6331,hAPP(X6331,fun(fun(X6329,bool),X6331),hAPP(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331))),finite_fold_image(X6331,X6329),times_times(X6331)),X6333),X6332),X6337)
        | hBOOL(hAPP(fun(X6329,bool),bool,hAPP(X6329,fun(fun(X6329,bool),bool),member(X6329),esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338)),X6337))
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,finite_finite_1(X6330),X6338))
        | ~ comm_monoid_mult(X6331) )
      & ( ~ hBOOL(hAPP(fun(X6329,bool),bool,hAPP(X6329,fun(fun(X6329,bool),bool),member(X6329),hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))),X6337))
        | hAPP(X6329,X6330,X6336,hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != ti(X6330,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | hAPP(X6329,X6331,X6333,hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != hAPP(X6330,X6331,X6334,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | hAPP(fun(X6330,bool),X6331,hAPP(X6331,fun(fun(X6330,bool),X6331),hAPP(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331))),finite_fold_image(X6331,X6330),times_times(X6331)),X6334),X6332),X6338) = hAPP(fun(X6329,bool),X6331,hAPP(X6331,fun(fun(X6329,bool),X6331),hAPP(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331))),finite_fold_image(X6331,X6329),times_times(X6331)),X6333),X6332),X6337)
        | hBOOL(hAPP(fun(X6329,bool),bool,hAPP(X6329,fun(fun(X6329,bool),bool),member(X6329),esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338)),X6337))
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,finite_finite_1(X6330),X6338))
        | ~ comm_monoid_mult(X6331) )
      & ( hBOOL(hAPP(fun(X6330,bool),bool,hAPP(X6330,fun(fun(X6330,bool),bool),member(X6330),esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338)),X6338))
        | hAPP(fun(X6330,bool),X6331,hAPP(X6331,fun(fun(X6330,bool),X6331),hAPP(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331))),finite_fold_image(X6331,X6330),times_times(X6331)),X6334),X6332),X6338) = hAPP(fun(X6329,bool),X6331,hAPP(X6331,fun(fun(X6329,bool),X6331),hAPP(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331))),finite_fold_image(X6331,X6329),times_times(X6331)),X6333),X6332),X6337)
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,hAPP(X6330,fun(fun(X6330,bool),bool),member(X6330),hAPP(X6329,X6330,X6336,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))),X6338))
        | hAPP(X6330,X6329,X6335,hAPP(X6329,X6330,X6336,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != ti(X6329,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,finite_finite_1(X6330),X6338))
        | ~ comm_monoid_mult(X6331) )
      & ( ~ hBOOL(hAPP(fun(X6329,bool),bool,hAPP(X6329,fun(fun(X6329,bool),bool),member(X6329),hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))),X6337))
        | hAPP(X6329,X6330,X6336,hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != ti(X6330,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | hAPP(X6329,X6331,X6333,hAPP(X6330,X6329,X6335,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != hAPP(X6330,X6331,X6334,esk144_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | hAPP(fun(X6330,bool),X6331,hAPP(X6331,fun(fun(X6330,bool),X6331),hAPP(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6330,X6331),fun(X6331,fun(fun(X6330,bool),X6331))),finite_fold_image(X6331,X6330),times_times(X6331)),X6334),X6332),X6338) = hAPP(fun(X6329,bool),X6331,hAPP(X6331,fun(fun(X6329,bool),X6331),hAPP(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331)),hAPP(fun(X6331,fun(X6331,X6331)),fun(fun(X6329,X6331),fun(X6331,fun(fun(X6329,bool),X6331))),finite_fold_image(X6331,X6329),times_times(X6331)),X6333),X6332),X6337)
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,hAPP(X6330,fun(fun(X6330,bool),bool),member(X6330),hAPP(X6329,X6330,X6336,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))),X6338))
        | hAPP(X6330,X6329,X6335,hAPP(X6329,X6330,X6336,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))) != ti(X6329,esk143_10(X6329,X6330,X6331,X6332,X6333,X6334,X6335,X6336,X6337,X6338))
        | ~ hBOOL(hAPP(fun(X6330,bool),bool,finite_finite_1(X6330),X6338))
        | ~ comm_monoid_mult(X6331) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_710_fold__image__eq__general__inverses])])])])]) ).

fof(i_0_1182,plain,
    ~ ! [X44] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
       => ( ! [X33] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_94__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_1183,plain,
    ! [X2,X1,X38,X40] :
      ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => ( 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),X38),X40)))
       => ? [X26] :
            ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X40))
            & ~ 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),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)),X40))),hAPP(X2,fun(X1,bool),hAPP(fun(X1,fun(X2,bool)),fun(X2,fun(X1,bool)),combc(X1,X2,bool),hAPP(fun(X1,X2),fun(X1,fun(X2,bool)),hAPP(fun(X2,fun(X2,bool)),fun(fun(X1,X2),fun(X1,fun(X2,bool))),combb(X2,fun(X2,bool),X1),fequal(X2)),X38)),hAPP(X1,X2,X38,X26)))))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_521_pigeonhole__infinite]) ).

fof(i_0_1184,plain,
    ! [X29,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)),X29)))) = 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,X29))))) ),
    inference(fof_simplification,[status(thm)],[fact_428_card__less__Suc2]) ).

fof(i_0_1185,plain,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X15,X14,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
            & ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_988_setsum__delta]) ).

fof(i_0_1186,plain,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X15,X14,X41] :
          ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X41))
         => ( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = hAPP(X1,X2,X15,X14) )
            & ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X41))
             => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),hAPP(X2,fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(X2,fun(X1,X2)),combc(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),hAPP(X1,fun(X1,bool),fequal(X1),X14))),X15)),zero_zero(X2))),X41) = zero_zero(X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_987_setsum__delta_H]) ).

fof(i_0_1187,plain,
    ! [X3925,X3926,X3927,X3928,X3929,X3930] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3926)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3925)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3926,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3925,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3925),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3926),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3930) = ti(arrow_2142409994le_alt,X3927)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3927) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3930) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3925)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3926)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3926,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3925,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3925),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3926),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3930) = ti(arrow_2142409994le_alt,X3927)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3927) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3930) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3926)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3925)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3926,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3925,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3925),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3926),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3930) = ti(arrow_2142409994le_alt,X3927)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3927) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3930) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3925)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3926)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3929),X3930)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3926,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3927),X3928)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3925,esk1_6(X3925,X3926,X3927,X3928,X3929,X3930))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3925),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3926),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3930) = ti(arrow_2142409994le_alt,X3927)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3927) = ti(arrow_2142409994le_alt,X3928)
        | ti(arrow_2142409994le_alt,X3929) = ti(arrow_2142409994le_alt,X3930) ) ),
    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_1188,plain,
    ! [X3932,X3933,X3934,X3935,X3936,X3937] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3936),X3937)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3933,esk2_6(X3932,X3933,X3934,X3935,X3936,X3937))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3934),X3935)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3932,esk2_6(X3932,X3933,X3934,X3935,X3936,X3937))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3936),X3937)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3933)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3934),X3935)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3932)))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3932),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3933),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3937) = ti(arrow_2142409994le_alt,X3934)
        | ti(arrow_2142409994le_alt,X3936) = ti(arrow_2142409994le_alt,X3935)
        | ti(arrow_2142409994le_alt,X3934) = ti(arrow_2142409994le_alt,X3935)
        | ti(arrow_2142409994le_alt,X3936) = ti(arrow_2142409994le_alt,X3937) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3936),X3937)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3933,esk2_6(X3932,X3933,X3934,X3935,X3936,X3937))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3934),X3935)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3932,esk2_6(X3932,X3933,X3934,X3935,X3936,X3937))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3936),X3937)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3933)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3934),X3935)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3932)))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3932),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3933),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3937) = ti(arrow_2142409994le_alt,X3934)
        | ti(arrow_2142409994le_alt,X3936) = ti(arrow_2142409994le_alt,X3935)
        | ti(arrow_2142409994le_alt,X3934) = ti(arrow_2142409994le_alt,X3935)
        | ti(arrow_2142409994le_alt,X3936) = ti(arrow_2142409994le_alt,X3937) ) ),
    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_1189,plain,
    ! [X3945,X3946,X3947,X3948,X3949,X3950] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3946)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3945)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3946,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3945,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3945),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3946),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3947) = ti(arrow_2142409994le_alt,X3948)
        | ti(arrow_2142409994le_alt,X3949) = ti(arrow_2142409994le_alt,X3950) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3945)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3946)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3946,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3945,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3945),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3946),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3947) = ti(arrow_2142409994le_alt,X3948)
        | ti(arrow_2142409994le_alt,X3949) = ti(arrow_2142409994le_alt,X3950) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3946)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3945)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3946,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3945,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3945),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3946),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3947) = ti(arrow_2142409994le_alt,X3948)
        | ti(arrow_2142409994le_alt,X3949) = ti(arrow_2142409994le_alt,X3950) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3945)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3946)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3949),X3950)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3946,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3947),X3948)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3945,esk4_6(X3945,X3946,X3947,X3948,X3949,X3950))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3945),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3946),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3947) = ti(arrow_2142409994le_alt,X3948)
        | ti(arrow_2142409994le_alt,X3949) = ti(arrow_2142409994le_alt,X3950) ) ),
    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_1190,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_84__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_1191,plain,
    ! [X16] :
      ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_1998540521e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_1998540521e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1192,plain,
    ! [X3939,X3940,X3941,X3942,X3943] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3940)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3939)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3940,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3939,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3939),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3940),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3943) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3943) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3939)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3940)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3940,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3939,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3939),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3940),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3943) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3943) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3940)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3939)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3940,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3939,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3939),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3940),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3943) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3943) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3939)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3940)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3942),X3943)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3940,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3943),X3941)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3939,esk3_5(X3939,X3940,X3941,X3942,X3943))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3939),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3940),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3943) = ti(arrow_2142409994le_alt,X3941)
        | ti(arrow_2142409994le_alt,X3942) = ti(arrow_2142409994le_alt,X3943) ) ),
    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_1193,plain,
    ! [X4151,X4152] :
      ( ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk24_2(X4151,X4152)),arrow_301600364e_Prof))
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4152),X4151))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4152),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
      & ( ti(arrow_2142409994le_alt,esk25_2(X4151,X4152)) != ti(arrow_2142409994le_alt,esk26_2(X4151,X4152))
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4152),X4151))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4152),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X4151,X4152)),esk26_2(X4151,X4152))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk24_2(X4151,X4152),X4151)))
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4152),X4151))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4152),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X4151,X4152)),esk26_2(X4151,X4152))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4152,esk24_2(X4151,X4152))))
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4152),X4151))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4152),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_81_dictatorI])])])]) ).

fof(i_0_1194,plain,
    ! [X4033] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4033) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4033)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4033)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1167])])]) ).

fof(i_0_1195,plain,
    ! [X3952,X3953,X3954,X3955] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3953)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3952)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3953,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3952,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3952),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3953),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3954) = ti(arrow_2142409994le_alt,X3955) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3952)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3953)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3953,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3952,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3952),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3953),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3954) = ti(arrow_2142409994le_alt,X3955) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3953)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3952)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3953,esk5_4(X3952,X3953,X3954,X3955))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3952,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3952),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3953),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3954) = ti(arrow_2142409994le_alt,X3955) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3952)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3953)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3954),X3955)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3953,esk5_4(X3952,X3953,X3954,X3955))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3955),X3954)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3952,esk5_4(X3952,X3953,X3954,X3955))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3952),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3953),arrow_301600364e_Prof))
        | ti(arrow_2142409994le_alt,X3954) = ti(arrow_2142409994le_alt,X3955) ) ),
    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_1196,plain,
    ! [X4182,X4183,X4184,X4185,X4186] :
      ( ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4183)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4185)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4186)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4186),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4185)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4186)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4186)
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4186),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4186),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) = ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4186)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ti(arrow_2142409994le_alt,X4183) != ti(arrow_2142409994le_alt,X4186)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ti(arrow_2142409994le_alt,X4182) != ti(arrow_2142409994le_alt,X4185)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4186),X4183)),X4184))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),X4184))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4186),X4183)),X4184))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4186)),X4184))
        | ti(arrow_2142409994le_alt,X4182) = ti(arrow_2142409994le_alt,X4183)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4182),X4183)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4184),X4185),X4186)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4184),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4185) = ti(arrow_2142409994le_alt,X4186) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_in__below])])]) ).

fof(i_0_1197,plain,
    ! [X4132,X4133,X4134,X4135,X4136] :
      ( ( ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4133)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4136)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4135)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4135)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) = ti(arrow_2142409994le_alt,X4136)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4133) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4133) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4135)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4135)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4135)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4135)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4133) = ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4133) = ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4135)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) != ti(arrow_2142409994le_alt,X4135)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ti(arrow_2142409994le_alt,X4133) != ti(arrow_2142409994le_alt,X4136)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4135)),X4134))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),X4134))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4135)),X4134))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4135),X4133)),X4134))
        | ti(arrow_2142409994le_alt,X4132) = ti(arrow_2142409994le_alt,X4133)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4132),X4133)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4134),X4135),X4136)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4134),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4135) = ti(arrow_2142409994le_alt,X4136) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_in__above])])]) ).

fof(i_0_1198,plain,
    ! [X6240,X6241,X6242] :
      ( ( ti(X6240,X6241) = zero_zero(X6240)
        | ~ hBOOL(hAPP(X6240,bool,hAPP(X6240,fun(X6240,bool),ord_less_eq(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),plus_plus(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6241),X6241)),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6242),X6242))),zero_zero(X6240)))
        | ~ linord581940658strict(X6240) )
      & ( ti(X6240,X6242) = zero_zero(X6240)
        | ~ hBOOL(hAPP(X6240,bool,hAPP(X6240,fun(X6240,bool),ord_less_eq(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),plus_plus(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6241),X6241)),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6242),X6242))),zero_zero(X6240)))
        | ~ linord581940658strict(X6240) )
      & ( ti(X6240,X6241) != zero_zero(X6240)
        | ti(X6240,X6242) != zero_zero(X6240)
        | hBOOL(hAPP(X6240,bool,hAPP(X6240,fun(X6240,bool),ord_less_eq(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),plus_plus(X6240),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6241),X6241)),hAPP(X6240,X6240,hAPP(X6240,fun(X6240,X6240),times_times(X6240),X6242),X6242))),zero_zero(X6240)))
        | ~ linord581940658strict(X6240) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_686_sum__squares__le__zero__iff])])])]) ).

fof(i_0_1199,plain,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X34,X35] : ~ 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),times_times(X1),X34),X34)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X35),X35))),zero_zero(X1))) ),
    inference(fof_simplification,[status(thm)],[fact_688_not__sum__squares__lt__zero]) ).

fof(i_0_1200,plain,
    ! [X4137,X4138,X4139,X4140,X4143,X4144,X4145,X4146,X4147,X4148,X4149,X4150] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(X4137,X4138),bool),bool,hAPP(product_prod(X4137,X4138),fun(fun(product_prod(X4137,X4138),bool),bool),member(product_prod(X4137,X4138)),hAPP(X4138,product_prod(X4137,X4138),hAPP(X4137,fun(X4138,product_prod(X4137,X4138)),product_Pair(X4137,X4138),esk22_4(X4137,X4138,X4139,X4140)),esk23_4(X4137,X4138,X4139,X4140))),X4140))
        | ~ hBOOL(hAPP(fun(product_prod(X4137,X4138),bool),bool,hAPP(product_prod(X4137,X4138),fun(fun(product_prod(X4137,X4138),bool),bool),member(product_prod(X4137,X4138)),hAPP(X4138,product_prod(X4137,X4138),hAPP(X4137,fun(X4138,product_prod(X4137,X4138)),product_Pair(X4137,X4138),esk22_4(X4137,X4138,X4139,X4140)),esk23_4(X4137,X4138,X4139,X4140))),X4139))
        | ti(fun(product_prod(X4137,X4138),bool),X4140) = ti(fun(product_prod(X4137,X4138),bool),X4139) )
      & ( hBOOL(hAPP(fun(product_prod(X4137,X4138),bool),bool,hAPP(product_prod(X4137,X4138),fun(fun(product_prod(X4137,X4138),bool),bool),member(product_prod(X4137,X4138)),hAPP(X4138,product_prod(X4137,X4138),hAPP(X4137,fun(X4138,product_prod(X4137,X4138)),product_Pair(X4137,X4138),esk22_4(X4137,X4138,X4139,X4140)),esk23_4(X4137,X4138,X4139,X4140))),X4140))
        | hBOOL(hAPP(fun(product_prod(X4137,X4138),bool),bool,hAPP(product_prod(X4137,X4138),fun(fun(product_prod(X4137,X4138),bool),bool),member(product_prod(X4137,X4138)),hAPP(X4138,product_prod(X4137,X4138),hAPP(X4137,fun(X4138,product_prod(X4137,X4138)),product_Pair(X4137,X4138),esk22_4(X4137,X4138,X4139,X4140)),esk23_4(X4137,X4138,X4139,X4140))),X4139))
        | ti(fun(product_prod(X4137,X4138),bool),X4140) = ti(fun(product_prod(X4137,X4138),bool),X4139) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X4143,X4144),bool),bool,hAPP(product_prod(X4143,X4144),fun(fun(product_prod(X4143,X4144),bool),bool),member(product_prod(X4143,X4144)),hAPP(X4144,product_prod(X4143,X4144),hAPP(X4143,fun(X4144,product_prod(X4143,X4144)),product_Pair(X4143,X4144),X4147),X4148)),X4146))
        | hBOOL(hAPP(fun(product_prod(X4143,X4144),bool),bool,hAPP(product_prod(X4143,X4144),fun(fun(product_prod(X4143,X4144),bool),bool),member(product_prod(X4143,X4144)),hAPP(X4144,product_prod(X4143,X4144),hAPP(X4143,fun(X4144,product_prod(X4143,X4144)),product_Pair(X4143,X4144),X4147),X4148)),X4145))
        | ti(fun(product_prod(X4143,X4144),bool),X4146) != ti(fun(product_prod(X4143,X4144),bool),X4145) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X4143,X4144),bool),bool,hAPP(product_prod(X4143,X4144),fun(fun(product_prod(X4143,X4144),bool),bool),member(product_prod(X4143,X4144)),hAPP(X4144,product_prod(X4143,X4144),hAPP(X4143,fun(X4144,product_prod(X4143,X4144)),product_Pair(X4143,X4144),X4149),X4150)),X4145))
        | hBOOL(hAPP(fun(product_prod(X4143,X4144),bool),bool,hAPP(product_prod(X4143,X4144),fun(fun(product_prod(X4143,X4144),bool),bool),member(product_prod(X4143,X4144)),hAPP(X4144,product_prod(X4143,X4144),hAPP(X4143,fun(X4144,product_prod(X4143,X4144)),product_Pair(X4143,X4144),X4149),X4150)),X4146))
        | ti(fun(product_prod(X4143,X4144),bool),X4146) != ti(fun(product_prod(X4143,X4144),bool),X4145) ) ),
    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_80_pred__equals__eq2])])])])])]) ).

fof(i_0_1201,plain,
    ! [X5730,X5731,X5732,X5733,X5734] :
      ( hAPP(fun(X5730,bool),fun(X5731,bool),hAPP(fun(X5730,X5731),fun(fun(X5730,bool),fun(X5731,bool)),image(X5730,X5731),X5732),X5733) != ti(fun(X5731,bool),X5734)
      | hBOOL(hAPP(fun(fun(X5731,X5730),bool),bool,hAPP(fun(X5731,X5730),fun(fun(fun(X5731,X5730),bool),bool),member(fun(X5731,X5730)),hAPP(fun(X5731,bool),fun(X5731,X5730),hAPP(fun(X5731,X5730),fun(fun(X5731,bool),fun(X5731,X5730)),restrict(X5731,X5730),hAPP(fun(X5730,X5731),fun(X5731,X5730),hAPP(fun(X5730,bool),fun(fun(X5730,X5731),fun(X5731,X5730)),hilbert_inv_into(X5730,X5731),X5733),X5732)),X5734)),hAPP(fun(X5731,fun(X5730,bool)),fun(fun(X5731,X5730),bool),hAPP(fun(X5731,bool),fun(fun(X5731,fun(X5730,bool)),fun(fun(X5731,X5730),bool)),pi(X5731,X5730),X5734),hAPP(fun(X5730,bool),fun(X5731,fun(X5730,bool)),combk(fun(X5730,bool),X5731),X5733)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_546_inv__into__funcset])]) ).

fof(i_0_1202,plain,
    ! [X6353,X6354,X6355,X6356,X6357,X6358] :
      ( ( hBOOL(hAPP(fun(X6354,bool),bool,hAPP(X6354,fun(fun(X6354,bool),bool),member(X6354),esk147_6(X6353,X6354,X6355,X6356,X6357,X6358)),X6358))
        | hAPP(fun(X6354,bool),fun(X6353,bool),hAPP(fun(X6354,X6353),fun(fun(X6354,bool),fun(X6353,bool)),image(X6354,X6353),X6355),X6357) = hAPP(fun(X6354,bool),fun(X6353,bool),hAPP(fun(X6354,X6353),fun(fun(X6354,bool),fun(X6353,bool)),image(X6354,X6353),X6356),X6358)
        | ti(fun(X6354,bool),X6357) != ti(fun(X6354,bool),X6358) )
      & ( hAPP(X6354,X6353,X6355,esk147_6(X6353,X6354,X6355,X6356,X6357,X6358)) != hAPP(X6354,X6353,X6356,esk147_6(X6353,X6354,X6355,X6356,X6357,X6358))
        | hAPP(fun(X6354,bool),fun(X6353,bool),hAPP(fun(X6354,X6353),fun(fun(X6354,bool),fun(X6353,bool)),image(X6354,X6353),X6355),X6357) = hAPP(fun(X6354,bool),fun(X6353,bool),hAPP(fun(X6354,X6353),fun(fun(X6354,bool),fun(X6353,bool)),image(X6354,X6353),X6356),X6358)
        | ti(fun(X6354,bool),X6357) != ti(fun(X6354,bool),X6358) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_713_image__cong])])])]) ).

fof(i_0_1203,plain,
    ! [X4964,X4965,X4966,X4967,X4968,X4969,X4970] :
      ( ~ hBOOL(hAPP(fun(fun(X4964,bool),X4965),bool,hAPP(fun(X4964,X4965),fun(fun(fun(X4964,bool),X4965),bool),hAPP(X4965,fun(fun(X4964,X4965),fun(fun(fun(X4964,bool),X4965),bool)),hAPP(fun(X4965,fun(X4965,X4965)),fun(X4965,fun(fun(X4964,X4965),fun(fun(fun(X4964,bool),X4965),bool))),finite908156982e_idem(X4965,X4964),X4967),X4968),X4969),X4970))
      | hAPP(X4965,X4965,hAPP(X4965,fun(X4965,X4965),X4967,X4966),X4966) = ti(X4965,X4966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_folding__image__simple__idem_Oidem])]) ).

fof(i_0_1204,plain,
    ! [X4365,X4366,X4367] :
      ( ti(arrow_2142409994le_alt,X4366) = ti(arrow_2142409994le_alt,X4367)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4365),arrow_1568854078le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4365),X4366),X4367)),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_below__Lin])]) ).

fof(i_0_1205,plain,
    ! [X4045,X4046,X4047] :
      ( ti(arrow_2142409994le_alt,X4046) = ti(arrow_2142409994le_alt,X4047)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4045),arrow_1568854078le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4045),X4046),X4047)),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_above__Lin])]) ).

fof(i_0_1206,plain,
    ! [X1,X2,X38,X40] :
      ( 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),X38),X40))),hAPP(fun(X2,bool),nat,finite_card(X2),X40)))
     => ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X38),X40)) ),
    inference(fof_simplification,[status(thm)],[fact_501_pigeonhole]) ).

fof(i_0_1207,plain,
    ! [X6243,X6244,X6245] :
      ( ( ~ hBOOL(hAPP(X6243,bool,hAPP(X6243,fun(X6243,bool),ord_less(X6243),zero_zero(X6243)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),plus_plus(X6243),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6244),X6244)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6245),X6245))))
        | ti(X6243,X6244) != zero_zero(X6243)
        | ti(X6243,X6245) != zero_zero(X6243)
        | ~ linord581940658strict(X6243) )
      & ( ti(X6243,X6244) = zero_zero(X6243)
        | hBOOL(hAPP(X6243,bool,hAPP(X6243,fun(X6243,bool),ord_less(X6243),zero_zero(X6243)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),plus_plus(X6243),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6244),X6244)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6245),X6245))))
        | ~ linord581940658strict(X6243) )
      & ( ti(X6243,X6245) = zero_zero(X6243)
        | hBOOL(hAPP(X6243,bool,hAPP(X6243,fun(X6243,bool),ord_less(X6243),zero_zero(X6243)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),plus_plus(X6243),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6244),X6244)),hAPP(X6243,X6243,hAPP(X6243,fun(X6243,X6243),times_times(X6243),X6245),X6245))))
        | ~ linord581940658strict(X6243) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_687_sum__squares__gt__zero__iff])])])]) ).

fof(i_0_1208,plain,
    ! [X4035,X4036,X4037] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4035),X4036)),X4037))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4036),X4035)),X4037))
        | ti(arrow_2142409994le_alt,X4035) = ti(arrow_2142409994le_alt,X4036)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4037),arrow_1568854078le_Lin)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4036),X4035)),X4037))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4035),X4036)),X4037))
        | ti(arrow_2142409994le_alt,X4035) = ti(arrow_2142409994le_alt,X4036)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4037),arrow_1568854078le_Lin)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1168])])]) ).

fof(i_0_1209,plain,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X8),arrow_1568854078le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X15),X14)),X8)) ) ),
    inference(fof_simplification,[status(thm)],[fact_48_Lin__irrefl]) ).

fof(i_0_1210,plain,
    ! [X5851,X5852,X5853,X5854,X5855] :
      ( ~ hBOOL(hAPP(fun(fun(X5851,X5852),bool),bool,hAPP(fun(X5851,X5852),fun(fun(fun(X5851,X5852),bool),bool),member(fun(X5851,X5852)),X5853),hAPP(fun(X5851,fun(X5852,bool)),fun(fun(X5851,X5852),bool),hAPP(fun(X5851,bool),fun(fun(X5851,fun(X5852,bool)),fun(fun(X5851,X5852),bool)),pi(X5851,X5852),X5854),hAPP(fun(X5852,bool),fun(X5851,fun(X5852,bool)),combk(fun(X5852,bool),X5851),X5855))))
      | ~ hBOOL(hAPP(fun(fun(X5851,X5852),bool),bool,hAPP(fun(X5851,X5852),fun(fun(fun(X5851,X5852),bool),bool),member(fun(X5851,X5852)),X5853),hAPP(fun(X5851,bool),fun(fun(X5851,X5852),bool),extensional(X5851,X5852),X5854)))
      | hAPP(fun(X5851,X5852),fun(X5851,X5852),hAPP(fun(X5852,X5852),fun(fun(X5851,X5852),fun(X5851,X5852)),hAPP(fun(X5851,bool),fun(fun(X5852,X5852),fun(fun(X5851,X5852),fun(X5851,X5852))),compose(X5851,X5852,X5852),X5854),hAPP(fun(X5852,bool),fun(X5852,X5852),hAPP(fun(X5852,X5852),fun(fun(X5852,bool),fun(X5852,X5852)),restrict(X5852,X5852),combi(X5852)),X5855)),X5853) = ti(fun(X5851,X5852),X5853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_569_Id__compose])]) ).

fof(i_0_1211,plain,
    ! [X3917,X3918,X3919,X3920] :
      ( ( ti(arrow_2142409994le_alt,X3918) != ti(arrow_2142409994le_alt,X3920)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ti(arrow_2142409994le_alt,X3917) != ti(arrow_2142409994le_alt,X3920)
        | ti(arrow_2142409994le_alt,X3917) != ti(arrow_2142409994le_alt,X3918)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ti(arrow_2142409994le_alt,X3917) = ti(arrow_2142409994le_alt,X3920)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),X3919))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ti(arrow_2142409994le_alt,X3917) != ti(arrow_2142409994le_alt,X3920)
        | ti(arrow_2142409994le_alt,X3917) = ti(arrow_2142409994le_alt,X3920)
        | ti(arrow_2142409994le_alt,X3918) = ti(arrow_2142409994le_alt,X3920)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),X3919))
        | ti(arrow_2142409994le_alt,X3917) = ti(arrow_2142409994le_alt,X3920)
        | ti(arrow_2142409994le_alt,X3918) = ti(arrow_2142409994le_alt,X3920)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ti(arrow_2142409994le_alt,X3917) != ti(arrow_2142409994le_alt,X3920)
        | ti(arrow_2142409994le_alt,X3917) = ti(arrow_2142409994le_alt,X3918)
        | ti(arrow_2142409994le_alt,X3918) = ti(arrow_2142409994le_alt,X3920)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),X3919))
        | ti(arrow_2142409994le_alt,X3917) = ti(arrow_2142409994le_alt,X3918)
        | ti(arrow_2142409994le_alt,X3918) = ti(arrow_2142409994le_alt,X3920)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3917),X3918)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3919),X3920))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_in__mkbot])])]) ).

fof(i_0_1212,plain,
    ! [X3921,X3922,X3923,X3924] :
      ( ( ti(arrow_2142409994le_alt,X3921) != ti(arrow_2142409994le_alt,X3924)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ti(arrow_2142409994le_alt,X3922) != ti(arrow_2142409994le_alt,X3924)
        | ti(arrow_2142409994le_alt,X3921) != ti(arrow_2142409994le_alt,X3922)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ti(arrow_2142409994le_alt,X3922) = ti(arrow_2142409994le_alt,X3924)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),X3923))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ti(arrow_2142409994le_alt,X3922) != ti(arrow_2142409994le_alt,X3924)
        | ti(arrow_2142409994le_alt,X3922) = ti(arrow_2142409994le_alt,X3924)
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3924)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),X3923))
        | ti(arrow_2142409994le_alt,X3922) = ti(arrow_2142409994le_alt,X3924)
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3924)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ti(arrow_2142409994le_alt,X3922) != ti(arrow_2142409994le_alt,X3924)
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3922)
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3924)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),X3923))
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3922)
        | ti(arrow_2142409994le_alt,X3921) = ti(arrow_2142409994le_alt,X3924)
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3921),X3922)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3923),X3924))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_in__mktop])])]) ).

fof(i_0_1213,plain,
    ! [X5846,X5847,X5848,X5849,X5850] :
      ( ~ hBOOL(hAPP(fun(fun(X5846,X5847),bool),bool,hAPP(fun(X5846,X5847),fun(fun(fun(X5846,X5847),bool),bool),member(fun(X5846,X5847)),X5848),hAPP(fun(X5846,fun(X5847,bool)),fun(fun(X5846,X5847),bool),hAPP(fun(X5846,bool),fun(fun(X5846,fun(X5847,bool)),fun(fun(X5846,X5847),bool)),pi(X5846,X5847),X5849),hAPP(fun(X5847,bool),fun(X5846,fun(X5847,bool)),combk(fun(X5847,bool),X5846),X5850))))
      | ~ hBOOL(hAPP(fun(fun(X5846,X5847),bool),bool,hAPP(fun(X5846,X5847),fun(fun(fun(X5846,X5847),bool),bool),member(fun(X5846,X5847)),X5848),hAPP(fun(X5846,bool),fun(fun(X5846,X5847),bool),extensional(X5846,X5847),X5849)))
      | hAPP(fun(X5846,X5846),fun(X5846,X5847),hAPP(fun(X5846,X5847),fun(fun(X5846,X5846),fun(X5846,X5847)),hAPP(fun(X5846,bool),fun(fun(X5846,X5847),fun(fun(X5846,X5846),fun(X5846,X5847))),compose(X5846,X5846,X5847),X5849),X5848),hAPP(fun(X5846,bool),fun(X5846,X5846),hAPP(fun(X5846,X5846),fun(fun(X5846,bool),fun(X5846,X5846)),restrict(X5846,X5846),combi(X5846)),X5849)) = ti(fun(X5846,X5847),X5848) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_568_compose__Id])]) ).

fof(i_0_1214,plain,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
    inference(fof_simplification,[status(thm)],[fact_856_sup2E]) ).

fof(i_0_1215,plain,
    ! [X2,X1,X40,X43,X6,X7] :
      ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(fun(X1,fun(X2,bool))),X40),X43),X6),X7))
     => ~ ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7))
         => ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7)) ) ),
    inference(fof_simplification,[status(thm)],[fact_972_inf2E]) ).

fof(i_0_1216,plain,
    ! [X5421,X5422,X5423,X5424,X5425,X5426] :
      ( hAPP(X5421,X5422,hAPP(fun(X5422,X5421),fun(X5421,X5422),hAPP(fun(X5422,bool),fun(fun(X5422,X5421),fun(X5421,X5422)),hilbert_inv_into(X5422,X5421),X5423),X5424),X5425) != hAPP(X5421,X5422,hAPP(fun(X5422,X5421),fun(X5421,X5422),hAPP(fun(X5422,bool),fun(fun(X5422,X5421),fun(X5421,X5422)),hilbert_inv_into(X5422,X5421),X5423),X5424),X5426)
      | ~ hBOOL(hAPP(fun(X5421,bool),bool,hAPP(X5421,fun(fun(X5421,bool),bool),member(X5421),X5425),hAPP(fun(X5422,bool),fun(X5421,bool),hAPP(fun(X5422,X5421),fun(fun(X5422,bool),fun(X5421,bool)),image(X5422,X5421),X5424),X5423)))
      | ~ hBOOL(hAPP(fun(X5421,bool),bool,hAPP(X5421,fun(fun(X5421,bool),bool),member(X5421),X5426),hAPP(fun(X5422,bool),fun(X5421,bool),hAPP(fun(X5422,X5421),fun(fun(X5422,bool),fun(X5421,bool)),image(X5422,X5421),X5424),X5423)))
      | ti(X5421,X5425) = ti(X5421,X5426) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_476_inv__into__injective])]) ).

fof(i_0_1217,plain,
    ! [X1] :
      ( order(X1)
     => ! [X14,X15,X17,X81] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
              | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
                & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81))
                & ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X14))
                  | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X81)) ) ) )
            & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X81)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_769_atLeastatMost__psubset__iff]) ).

fof(i_0_1218,plain,
    ! [X6341,X6342,X6343,X6344,X6345] :
      ( ( hBOOL(hAPP(fun(X6341,bool),bool,hAPP(X6341,fun(fun(X6341,bool),bool),member(X6341),esk145_5(X6341,X6342,X6343,X6344,X6345)),X6345))
        | ti(fun(X6341,X6342),X6344) = ti(fun(X6341,X6342),X6343)
        | ~ hBOOL(hAPP(fun(fun(X6341,X6342),bool),bool,hAPP(fun(X6341,X6342),fun(fun(fun(X6341,X6342),bool),bool),member(fun(X6341,X6342)),X6343),hAPP(fun(X6341,bool),fun(fun(X6341,X6342),bool),extensional(X6341,X6342),X6345)))
        | ~ hBOOL(hAPP(fun(fun(X6341,X6342),bool),bool,hAPP(fun(X6341,X6342),fun(fun(fun(X6341,X6342),bool),bool),member(fun(X6341,X6342)),X6344),hAPP(fun(X6341,bool),fun(fun(X6341,X6342),bool),extensional(X6341,X6342),X6345))) )
      & ( hAPP(X6341,X6342,X6344,esk145_5(X6341,X6342,X6343,X6344,X6345)) != hAPP(X6341,X6342,X6343,esk145_5(X6341,X6342,X6343,X6344,X6345))
        | ti(fun(X6341,X6342),X6344) = ti(fun(X6341,X6342),X6343)
        | ~ hBOOL(hAPP(fun(fun(X6341,X6342),bool),bool,hAPP(fun(X6341,X6342),fun(fun(fun(X6341,X6342),bool),bool),member(fun(X6341,X6342)),X6343),hAPP(fun(X6341,bool),fun(fun(X6341,X6342),bool),extensional(X6341,X6342),X6345)))
        | ~ hBOOL(hAPP(fun(fun(X6341,X6342),bool),bool,hAPP(fun(X6341,X6342),fun(fun(fun(X6341,X6342),bool),bool),member(fun(X6341,X6342)),X6344),hAPP(fun(X6341,bool),fun(fun(X6341,X6342),bool),extensional(X6341,X6342),X6345))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_711_extensionalityI])])])]) ).

fof(i_0_1219,plain,
    ! [X1] :
      ( order(X1)
     => ! [X14,X15,X17,X81] :
          ( 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_atLeastAtMost(X1),X14),X15)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X17),X81)))
        <=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X14),X15))
            | ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X14))
              & hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X81)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_762_atLeastatMost__subset__iff]) ).

fof(i_0_1220,plain,
    ! [X5510,X5511,X5512] :
      ( ~ hBOOL(hAPP(fun(X5510,bool),bool,finite_finite_1(X5510),X5512))
      | ~ hBOOL(hAPP(fun(X5510,bool),bool,hAPP(fun(X5510,bool),fun(fun(X5510,bool),bool),ord_less_eq(fun(X5510,bool)),hAPP(fun(X5510,bool),fun(X5510,bool),hAPP(fun(X5510,X5510),fun(fun(X5510,bool),fun(X5510,bool)),image(X5510,X5510),X5511),X5512)),X5512))
      | ~ hBOOL(hAPP(fun(X5510,bool),bool,hAPP(fun(X5510,X5510),fun(fun(X5510,bool),bool),inj_on(X5510,X5510),X5511),X5512))
      | hAPP(fun(X5510,bool),fun(X5510,bool),hAPP(fun(X5510,X5510),fun(fun(X5510,bool),fun(X5510,bool)),image(X5510,X5510),X5511),X5512) = ti(fun(X5510,bool),X5512) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_endo__inj__surj])]) ).

fof(i_0_1221,plain,
    ! [X1,X2,X6,X38,X40,X43] :
      ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X38),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),X40),X43)))
     => ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X38,X6)),hAPP(X1,fun(X2,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X40)) ) ),
    inference(fof_simplification,[status(thm)],[fact_87_PiE]) ).

fof(i_0_1222,plain,
    ! [X5813,X5814,X5815,X5816,X5817,X5818,X5819,X5820] :
      ( hAPP(fun(X5814,bool),fun(X5815,bool),hAPP(fun(X5814,X5815),fun(fun(X5814,bool),fun(X5815,bool)),image(X5814,X5815),X5818),X5819) != ti(fun(X5815,bool),X5820)
      | hAPP(fun(X5815,bool),fun(X5813,bool),hAPP(fun(X5815,X5813),fun(fun(X5815,bool),fun(X5813,bool)),image(X5815,X5813),X5816),X5820) != ti(fun(X5813,bool),X5817)
      | hAPP(fun(X5814,bool),fun(X5813,bool),hAPP(fun(X5814,X5813),fun(fun(X5814,bool),fun(X5813,bool)),image(X5814,X5813),hAPP(fun(X5814,X5815),fun(X5814,X5813),hAPP(fun(X5815,X5813),fun(fun(X5814,X5815),fun(X5814,X5813)),hAPP(fun(X5814,bool),fun(fun(X5815,X5813),fun(fun(X5814,X5815),fun(X5814,X5813))),compose(X5814,X5815,X5813),X5819),X5816),X5818)),X5819) = ti(fun(X5813,bool),X5817) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_564_surj__compose])]) ).

fof(i_0_1223,plain,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X30,X54] :
          ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
          & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X30)),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X54),X30))),hAPP(nat,X1,X38,hAPP(nat,nat,suc,X30))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_965_setsum__cl__ivl__Suc]) ).

fof(i_0_1224,plain,
    ! [X6482,X6483,X6484,X6485,X6486] :
      ( ~ hBOOL(hAPP(fun(X6483,bool),bool,hAPP(fun(X6483,X6484),fun(fun(X6483,bool),bool),inj_on(X6483,X6484),X6486),top_top(fun(X6483,bool))))
      | hAPP(fun(X6483,X6484),fun(X6483,X6482),hAPP(fun(X6484,X6482),fun(fun(X6483,X6484),fun(X6483,X6482)),comp(X6484,X6482,X6483),hAPP(fun(X6484,X6483),fun(X6484,X6482),hAPP(fun(X6483,X6482),fun(fun(X6484,X6483),fun(X6484,X6482)),comp(X6483,X6482,X6484),X6485),hAPP(fun(X6483,X6484),fun(X6484,X6483),hAPP(fun(X6483,bool),fun(fun(X6483,X6484),fun(X6484,X6483)),hilbert_inv_into(X6483,X6484),top_top(fun(X6483,bool))),X6486))),X6486) = ti(fun(X6483,X6482),X6485) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_736_o__inv__o__cancel])]) ).

fof(i_0_1225,plain,
    ! [X2,X1,X40,X43,X6,X7] :
      ( ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X43,X6),X7))
       => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X40,X6),X7)) )
     => hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(fun(X1,fun(X2,bool))),X40),X43),X6),X7)) ),
    inference(fof_simplification,[status(thm)],[fact_857_sup2CI]) ).

fof(i_0_1226,plain,
    ! [X5801,X5802,X5803,X5804,X5805] :
      ( hAPP(fun(X5801,bool),fun(X5802,bool),hAPP(fun(X5801,X5802),fun(fun(X5801,bool),fun(X5802,bool)),image(X5801,X5802),X5803),X5804) != ti(fun(X5802,bool),X5805)
      | hAPP(fun(X5802,X5801),fun(X5802,X5802),hAPP(fun(X5801,X5802),fun(fun(X5802,X5801),fun(X5802,X5802)),hAPP(fun(X5802,bool),fun(fun(X5801,X5802),fun(fun(X5802,X5801),fun(X5802,X5802))),compose(X5802,X5801,X5802),X5805),X5803),hAPP(fun(X5802,bool),fun(X5802,X5801),hAPP(fun(X5802,X5801),fun(fun(X5802,bool),fun(X5802,X5801)),restrict(X5802,X5801),hAPP(fun(X5801,X5802),fun(X5802,X5801),hAPP(fun(X5801,bool),fun(fun(X5801,X5802),fun(X5802,X5801)),hilbert_inv_into(X5801,X5802),X5804),X5803)),X5805)) = hAPP(fun(X5802,bool),fun(X5802,X5802),hAPP(fun(X5802,X5802),fun(fun(X5802,bool),fun(X5802,X5802)),restrict(X5802,X5802),combi(X5802)),X5805) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_562_compose__id__inv__into])]) ).

fof(i_0_1227,plain,
    ! [X5877,X5878,X5879,X5880,X5881] :
      ( ( hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5879)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5881)) != hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5881)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5879))
        | ti(X5877,X5878) = ti(X5877,X5880)
        | ti(X5877,X5879) = ti(X5877,X5881)
        | ~ semiri456707255roduct(X5877) )
      & ( ti(X5877,X5878) != ti(X5877,X5880)
        | hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5879)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5881)) = hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5881)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5879))
        | ~ semiri456707255roduct(X5877) )
      & ( ti(X5877,X5879) != ti(X5877,X5881)
        | hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5879)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5881)) = hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),plus_plus(X5877),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5878),X5881)),hAPP(X5877,X5877,hAPP(X5877,fun(X5877,X5877),times_times(X5877),X5880),X5879))
        | ~ semiri456707255roduct(X5877) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_577_crossproduct__eq])])])]) ).

fof(i_0_1228,plain,
    ! [X5890,X5891,X5892,X5893,X5894] :
      ( ( ti(X5890,X5893) = ti(X5890,X5894)
        | ti(X5890,X5891) = ti(X5890,X5892)
        | hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5891)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5892)) != hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5892)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5891))
        | ~ semiri456707255roduct(X5890) )
      & ( ti(X5890,X5893) != ti(X5890,X5894)
        | hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5891)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5892)) = hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5892)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5891))
        | ~ semiri456707255roduct(X5890) )
      & ( ti(X5890,X5891) != ti(X5890,X5892)
        | hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5891)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5892)) = hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),plus_plus(X5890),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5893),X5892)),hAPP(X5890,X5890,hAPP(X5890,fun(X5890,X5890),times_times(X5890),X5894),X5891))
        | ~ semiri456707255roduct(X5890) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_580_crossproduct__noteq])])])]) ).

fof(i_0_1229,plain,
    ! [X5778,X5779,X5780,X5781,X5782] :
      ( ~ hBOOL(hAPP(fun(X5778,bool),bool,hAPP(fun(X5778,X5779),fun(fun(X5778,bool),bool),inj_on(X5778,X5779),X5781),X5782))
      | ~ hBOOL(hAPP(fun(X5779,bool),bool,hAPP(X5779,fun(fun(X5779,bool),bool),member(X5779),X5780),hAPP(fun(X5778,bool),fun(X5779,bool),hAPP(fun(X5778,X5779),fun(fun(X5778,bool),fun(X5779,bool)),image(X5778,X5779),X5781),X5782)))
      | hAPP(X5778,X5779,X5781,hAPP(X5779,X5778,hAPP(fun(X5778,X5779),fun(X5779,X5778),hAPP(fun(X5778,bool),fun(fun(X5778,X5779),fun(X5779,X5778)),the_inv_into(X5778,X5779),X5782),X5781),X5780)) = ti(X5779,X5780) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_558_f__the__inv__into__f])]) ).

fof(i_0_1230,plain,
    ! [X5463,X5464,X5465,X5466,X5467,X5468] :
      ( hAPP(fun(X5463,bool),fun(X5464,bool),hAPP(fun(X5463,X5464),fun(fun(X5463,bool),fun(X5464,bool)),image(X5463,X5464),X5466),X5467) != ti(fun(X5464,bool),X5468)
      | ~ hBOOL(hAPP(fun(X5464,bool),bool,hAPP(fun(X5464,bool),fun(fun(X5464,bool),bool),ord_less_eq(fun(X5464,bool)),X5465),X5468))
      | hAPP(fun(X5463,bool),fun(X5464,bool),hAPP(fun(X5463,X5464),fun(fun(X5463,bool),fun(X5464,bool)),image(X5463,X5464),X5466),hAPP(fun(X5464,bool),fun(X5463,bool),hAPP(fun(X5464,X5463),fun(fun(X5464,bool),fun(X5463,bool)),image(X5464,X5463),hAPP(fun(X5463,X5464),fun(X5464,X5463),hAPP(fun(X5463,bool),fun(fun(X5463,X5464),fun(X5464,X5463)),hilbert_inv_into(X5463,X5464),X5467),X5466)),X5465)) = ti(fun(X5464,bool),X5465) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_484_image__inv__into__cancel])]) ).

fof(i_0_1231,plain,
    ! [X1] :
      ( comm_monoid_add(X1)
     => ! [X38,X30,X54] :
          ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = zero_zero(X1) )
          & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
           => hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),hAPP(nat,nat,suc,X30))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X38),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X54),X30))),hAPP(nat,X1,X38,X30)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_964_setsum__op__ivl__Suc]) ).

fof(i_0_1232,plain,
    ! [X5469,X5470,X5471,X5472] :
      ( hAPP(fun(X5469,bool),fun(X5470,bool),hAPP(fun(X5469,X5470),fun(fun(X5469,bool),fun(X5470,bool)),image(X5469,X5470),X5472),top_top(fun(X5469,bool))) != top_top(fun(X5470,bool))
      | hAPP(fun(X5469,bool),fun(X5470,bool),hAPP(fun(X5469,X5470),fun(fun(X5469,bool),fun(X5470,bool)),image(X5469,X5470),X5472),hAPP(fun(X5470,bool),fun(X5469,bool),hAPP(fun(X5470,X5469),fun(fun(X5470,bool),fun(X5469,bool)),image(X5470,X5469),hAPP(fun(X5469,X5470),fun(X5470,X5469),hAPP(fun(X5469,bool),fun(fun(X5469,X5470),fun(X5470,X5469)),hilbert_inv_into(X5469,X5470),top_top(fun(X5469,bool))),X5472)),X5471)) = ti(fun(X5470,bool),X5471) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_485_image__surj__f__inv__f])]) ).

fof(i_0_1233,plain,
    ! [X5411,X5412,X5413,X5414,X5415] :
      ( ~ hBOOL(hAPP(fun(X5411,bool),bool,hAPP(X5411,fun(fun(X5411,bool),bool),member(X5411),X5413),hAPP(fun(X5412,bool),fun(X5411,bool),hAPP(fun(X5412,X5411),fun(fun(X5412,bool),fun(X5411,bool)),image(X5412,X5411),X5414),X5415)))
      | hAPP(X5412,X5411,X5414,hAPP(X5411,X5412,hAPP(fun(X5412,X5411),fun(X5411,X5412),hAPP(fun(X5412,bool),fun(fun(X5412,X5411),fun(X5411,X5412)),hilbert_inv_into(X5412,X5411),X5415),X5414),X5413)) = ti(X5411,X5413) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_474_f__inv__into__f])]) ).

fof(i_0_1234,plain,
    ! [X5441,X5442,X5443,X5444,X5446,X5447] :
      ( ( ti(X5442,X5443) = hAPP(X5441,X5442,X5444,esk104_4(X5441,X5442,X5443,X5444))
        | ~ hBOOL(hAPP(fun(X5442,bool),bool,hAPP(X5442,fun(fun(X5442,bool),bool),member(X5442),X5443),hAPP(fun(X5441,bool),fun(X5442,bool),hAPP(fun(X5441,X5442),fun(fun(X5441,bool),fun(X5442,bool)),image(X5441,X5442),X5444),top_top(fun(X5441,bool)))))
        | ~ hBOOL(hAPP(fun(X5441,bool),bool,hAPP(fun(X5441,X5442),fun(fun(X5441,bool),bool),inj_on(X5441,X5442),X5444),top_top(fun(X5441,bool)))) )
      & ( ti(X5442,X5443) != hAPP(X5441,X5442,X5444,X5446)
        | ti(X5441,X5446) = ti(X5441,esk104_4(X5441,X5442,X5443,X5444))
        | ~ hBOOL(hAPP(fun(X5442,bool),bool,hAPP(X5442,fun(fun(X5442,bool),bool),member(X5442),X5443),hAPP(fun(X5441,bool),fun(X5442,bool),hAPP(fun(X5441,X5442),fun(fun(X5441,bool),fun(X5442,bool)),image(X5441,X5442),X5444),top_top(fun(X5441,bool)))))
        | ~ hBOOL(hAPP(fun(X5441,bool),bool,hAPP(fun(X5441,X5442),fun(fun(X5441,bool),bool),inj_on(X5441,X5442),X5444),top_top(fun(X5441,bool)))) )
      & ( ti(X5442,X5443) = hAPP(X5441,X5442,X5444,esk105_5(X5441,X5442,X5443,X5444,X5447))
        | ti(X5442,X5443) != hAPP(X5441,X5442,X5444,X5447)
        | hBOOL(hAPP(fun(X5442,bool),bool,hAPP(X5442,fun(fun(X5442,bool),bool),member(X5442),X5443),hAPP(fun(X5441,bool),fun(X5442,bool),hAPP(fun(X5441,X5442),fun(fun(X5441,bool),fun(X5442,bool)),image(X5441,X5442),X5444),top_top(fun(X5441,bool)))))
        | ~ hBOOL(hAPP(fun(X5441,bool),bool,hAPP(fun(X5441,X5442),fun(fun(X5441,bool),bool),inj_on(X5441,X5442),X5444),top_top(fun(X5441,bool)))) )
      & ( ti(X5441,esk105_5(X5441,X5442,X5443,X5444,X5447)) != ti(X5441,X5447)
        | ti(X5442,X5443) != hAPP(X5441,X5442,X5444,X5447)
        | hBOOL(hAPP(fun(X5442,bool),bool,hAPP(X5442,fun(fun(X5442,bool),bool),member(X5442),X5443),hAPP(fun(X5441,bool),fun(X5442,bool),hAPP(fun(X5441,X5442),fun(fun(X5441,bool),fun(X5442,bool)),image(X5441,X5442),X5444),top_top(fun(X5441,bool)))))
        | ~ hBOOL(hAPP(fun(X5441,bool),bool,hAPP(fun(X5441,X5442),fun(fun(X5441,bool),bool),inj_on(X5441,X5442),X5444),top_top(fun(X5441,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_range__ex1__eq])])])])]) ).

fof(i_0_1235,plain,
    ! [X5596,X5597,X5598,X5599,X5600] :
      ( ( hBOOL(hAPP(fun(X5596,bool),bool,hAPP(fun(X5596,bool),fun(fun(X5596,bool),bool),ord_less_eq(fun(X5596,bool)),esk111_5(X5596,X5597,X5598,X5599,X5600)),X5599))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,hAPP(fun(X5597,bool),fun(fun(X5597,bool),bool),ord_less_eq(fun(X5597,bool)),X5600),hAPP(fun(X5596,bool),fun(X5597,bool),hAPP(fun(X5596,X5597),fun(fun(X5596,bool),fun(X5597,bool)),image(X5596,X5597),X5598),X5599)))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,finite_finite_1(X5597),X5600)) )
      & ( hBOOL(hAPP(fun(X5596,bool),bool,finite_finite_1(X5596),esk111_5(X5596,X5597,X5598,X5599,X5600)))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,hAPP(fun(X5597,bool),fun(fun(X5597,bool),bool),ord_less_eq(fun(X5597,bool)),X5600),hAPP(fun(X5596,bool),fun(X5597,bool),hAPP(fun(X5596,X5597),fun(fun(X5596,bool),fun(X5597,bool)),image(X5596,X5597),X5598),X5599)))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,finite_finite_1(X5597),X5600)) )
      & ( ti(fun(X5597,bool),X5600) = hAPP(fun(X5596,bool),fun(X5597,bool),hAPP(fun(X5596,X5597),fun(fun(X5596,bool),fun(X5597,bool)),image(X5596,X5597),X5598),esk111_5(X5596,X5597,X5598,X5599,X5600))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,hAPP(fun(X5597,bool),fun(fun(X5597,bool),bool),ord_less_eq(fun(X5597,bool)),X5600),hAPP(fun(X5596,bool),fun(X5597,bool),hAPP(fun(X5596,X5597),fun(fun(X5596,bool),fun(X5597,bool)),image(X5596,X5597),X5598),X5599)))
        | ~ hBOOL(hAPP(fun(X5597,bool),bool,finite_finite_1(X5597),X5600)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_514_finite__subset__image])])])]) ).

fof(i_0_1236,plain,
    ! [X4878,X4879,X4880,X4881,X4882] :
      ( ( hBOOL(hAPP(fun(X4879,bool),bool,hAPP(X4879,fun(fun(X4879,bool),bool),member(X4879),esk69_5(X4878,X4879,X4880,X4881,X4882)),X4882))
        | hBOOL(hAPP(fun(X4879,bool),bool,hAPP(fun(X4879,X4878),fun(fun(X4879,bool),bool),inj_on(X4879,X4878),X4881),X4882)) )
      & ( hAPP(X4878,X4879,X4880,hAPP(X4879,X4878,X4881,esk69_5(X4878,X4879,X4880,X4881,X4882))) != ti(X4879,esk69_5(X4878,X4879,X4880,X4881,X4882))
        | hBOOL(hAPP(fun(X4879,bool),bool,hAPP(fun(X4879,X4878),fun(fun(X4879,bool),bool),inj_on(X4879,X4878),X4881),X4882)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_inj__on__inverseI])])])]) ).

fof(i_0_1237,plain,
    ! [X5538,X5539,X5540,X5541,X5542] :
      ( ~ hBOOL(hAPP(fun(X5538,bool),bool,hAPP(fun(X5538,X5539),fun(fun(X5538,bool),bool),inj_on(X5538,X5539),X5541),X5542))
      | ~ hBOOL(hAPP(fun(X5538,bool),bool,hAPP(fun(X5538,bool),fun(fun(X5538,bool),bool),ord_less_eq(fun(X5538,bool)),X5540),X5542))
      | hAPP(fun(X5539,bool),fun(X5538,bool),hAPP(fun(X5539,X5538),fun(fun(X5539,bool),fun(X5538,bool)),image(X5539,X5538),hAPP(fun(X5538,X5539),fun(X5539,X5538),hAPP(fun(X5538,bool),fun(fun(X5538,X5539),fun(X5539,X5538)),hilbert_inv_into(X5538,X5539),X5542),X5541)),hAPP(fun(X5538,bool),fun(X5539,bool),hAPP(fun(X5538,X5539),fun(fun(X5538,bool),fun(X5539,bool)),image(X5538,X5539),X5541),X5540)) = ti(fun(X5538,bool),X5540) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_502_inv__into__image__cancel])]) ).

fof(i_0_1238,plain,
    ! [X6696,X6697,X6698,X6699,X6700] :
      ( ( hAPP(fun(X6696,bool),fun(X6697,bool),hAPP(fun(X6696,X6697),fun(fun(X6696,bool),fun(X6697,bool)),image(X6696,X6697),X6698),X6699) != hAPP(fun(X6696,bool),fun(X6697,bool),hAPP(fun(X6696,X6697),fun(fun(X6696,bool),fun(X6697,bool)),image(X6696,X6697),X6698),X6700)
        | ti(fun(X6696,bool),X6699) = ti(fun(X6696,bool),X6700)
        | ~ hBOOL(hAPP(fun(X6696,bool),bool,hAPP(fun(X6696,X6697),fun(fun(X6696,bool),bool),inj_on(X6696,X6697),X6698),hAPP(fun(X6696,bool),fun(X6696,bool),hAPP(fun(X6696,bool),fun(fun(X6696,bool),fun(X6696,bool)),semilattice_sup_sup(fun(X6696,bool)),X6699),X6700))) )
      & ( ti(fun(X6696,bool),X6699) != ti(fun(X6696,bool),X6700)
        | hAPP(fun(X6696,bool),fun(X6697,bool),hAPP(fun(X6696,X6697),fun(fun(X6696,bool),fun(X6697,bool)),image(X6696,X6697),X6698),X6699) = hAPP(fun(X6696,bool),fun(X6697,bool),hAPP(fun(X6696,X6697),fun(fun(X6696,bool),fun(X6697,bool)),image(X6696,X6697),X6698),X6700)
        | ~ hBOOL(hAPP(fun(X6696,bool),bool,hAPP(fun(X6696,X6697),fun(fun(X6696,bool),bool),inj_on(X6696,X6697),X6698),hAPP(fun(X6696,bool),fun(X6696,bool),hAPP(fun(X6696,bool),fun(fun(X6696,bool),fun(X6696,bool)),semilattice_sup_sup(fun(X6696,bool)),X6699),X6700))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_780_inj__on__Un__image__eq__iff])])]) ).

fof(i_0_1239,plain,
    ! [X5344,X5345,X5346,X5347,X5348,X5350,X5351,X5352,X5353,X5354,X5355] :
      ( ( hBOOL(hAPP(fun(X5345,bool),bool,hAPP(fun(X5345,bool),fun(fun(X5345,bool),bool),ord_less_eq(fun(X5345,bool)),esk102_5(X5344,X5345,X5346,X5347,X5348)),X5348))
        | ~ hBOOL(hAPP(fun(X5344,bool),bool,hAPP(fun(X5344,bool),fun(fun(X5344,bool),bool),ord_less_eq(fun(X5344,bool)),X5346),hAPP(fun(X5345,bool),fun(X5344,bool),hAPP(fun(X5345,X5344),fun(fun(X5345,bool),fun(X5344,bool)),image(X5345,X5344),X5347),X5348))) )
      & ( ti(fun(X5344,bool),X5346) = hAPP(fun(X5345,bool),fun(X5344,bool),hAPP(fun(X5345,X5344),fun(fun(X5345,bool),fun(X5344,bool)),image(X5345,X5344),X5347),esk102_5(X5344,X5345,X5346,X5347,X5348))
        | ~ hBOOL(hAPP(fun(X5344,bool),bool,hAPP(fun(X5344,bool),fun(fun(X5344,bool),bool),ord_less_eq(fun(X5344,bool)),X5346),hAPP(fun(X5345,bool),fun(X5344,bool),hAPP(fun(X5345,X5344),fun(fun(X5345,bool),fun(X5344,bool)),image(X5345,X5344),X5347),X5348))) )
      & ( ~ hBOOL(hAPP(fun(X5351,bool),bool,hAPP(fun(X5351,bool),fun(fun(X5351,bool),bool),ord_less_eq(fun(X5351,bool)),X5355),X5354))
        | ti(fun(X5350,bool),X5352) != hAPP(fun(X5351,bool),fun(X5350,bool),hAPP(fun(X5351,X5350),fun(fun(X5351,bool),fun(X5350,bool)),image(X5351,X5350),X5353),X5355)
        | hBOOL(hAPP(fun(X5350,bool),bool,hAPP(fun(X5350,bool),fun(fun(X5350,bool),bool),ord_less_eq(fun(X5350,bool)),X5352),hAPP(fun(X5351,bool),fun(X5350,bool),hAPP(fun(X5351,X5350),fun(fun(X5351,bool),fun(X5350,bool)),image(X5351,X5350),X5353),X5354))) ) ),
    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_463_subset__image__iff])])])])])]) ).

fof(i_0_1240,plain,
    ! [X1] :
      ( semilattice_sup(X1)
     => ! [X21,X22,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X21),X22)),X34))
         => ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X21),X34))
             => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X22),X34)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_849_le__supE]) ).

fof(i_0_1241,plain,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    inference(fof_simplification,[status(thm)],[fact_774_UnE]) ).

fof(i_0_1242,plain,
    ! [X49,X50,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X49),X50)),X51))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X50),X51)) ) ),
    inference(fof_simplification,[status(thm)],[fact_193_add__leE]) ).

fof(i_0_1243,plain,
    ! [X5585,X5586,X5587,X5588,X5589] :
      ( ( ti(X5585,X5587) = hAPP(X5586,X5585,X5588,esk109_5(X5585,X5586,X5587,X5588,X5589))
        | ~ hBOOL(hAPP(fun(X5585,bool),bool,hAPP(X5585,fun(fun(X5585,bool),bool),member(X5585),X5587),hAPP(fun(X5586,bool),fun(X5585,bool),hAPP(fun(X5586,X5585),fun(fun(X5586,bool),fun(X5585,bool)),image(X5586,X5585),X5588),X5589))) )
      & ( hBOOL(hAPP(fun(X5586,bool),bool,hAPP(X5586,fun(fun(X5586,bool),bool),member(X5586),esk109_5(X5585,X5586,X5587,X5588,X5589)),X5589))
        | ~ hBOOL(hAPP(fun(X5585,bool),bool,hAPP(X5585,fun(fun(X5585,bool),bool),member(X5585),X5587),hAPP(fun(X5586,bool),fun(X5585,bool),hAPP(fun(X5586,X5585),fun(fun(X5586,bool),fun(X5585,bool)),image(X5586,X5585),X5588),X5589))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1169])])])]) ).

fof(i_0_1244,plain,
    ! [X5373,X5374,X5375,X5376,X5377,X5379,X5380,X5381,X5382,X5383,X5384] :
      ( ( hBOOL(hAPP(fun(X5374,bool),bool,hAPP(X5374,fun(fun(X5374,bool),bool),member(X5374),esk103_5(X5373,X5374,X5375,X5376,X5377)),X5377))
        | ~ hBOOL(hAPP(fun(X5373,bool),bool,hAPP(X5373,fun(fun(X5373,bool),bool),member(X5373),X5375),hAPP(fun(X5374,bool),fun(X5373,bool),hAPP(fun(X5374,X5373),fun(fun(X5374,bool),fun(X5373,bool)),image(X5374,X5373),X5376),X5377))) )
      & ( ti(X5373,X5375) = hAPP(X5374,X5373,X5376,esk103_5(X5373,X5374,X5375,X5376,X5377))
        | ~ hBOOL(hAPP(fun(X5373,bool),bool,hAPP(X5373,fun(fun(X5373,bool),bool),member(X5373),X5375),hAPP(fun(X5374,bool),fun(X5373,bool),hAPP(fun(X5374,X5373),fun(fun(X5374,bool),fun(X5373,bool)),image(X5374,X5373),X5376),X5377))) )
      & ( ~ hBOOL(hAPP(fun(X5380,bool),bool,hAPP(X5380,fun(fun(X5380,bool),bool),member(X5380),X5384),X5383))
        | ti(X5379,X5381) != hAPP(X5380,X5379,X5382,X5384)
        | hBOOL(hAPP(fun(X5379,bool),bool,hAPP(X5379,fun(fun(X5379,bool),bool),member(X5379),X5381),hAPP(fun(X5380,bool),fun(X5379,bool),hAPP(fun(X5380,X5379),fun(fun(X5380,bool),fun(X5379,bool)),image(X5380,X5379),X5382),X5383))) ) ),
    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_468_image__iff])])])])])]) ).

fof(i_0_1245,plain,
    ! [X1] :
      ( linordered_ring(X1)
     => ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X21),X21)),zero_zero(X1))) ),
    inference(fof_simplification,[status(thm)],[fact_636_not__square__less__zero]) ).

fof(i_0_1246,plain,
    ! [X4898,X4899,X4900] :
      ( ~ hBOOL(hAPP(fun(X4898,bool),bool,finite_finite_1(X4898),X4900))
      | ~ hBOOL(hAPP(fun(X4898,bool),bool,hAPP(fun(X4898,bool),fun(fun(X4898,bool),bool),ord_less_eq(fun(X4898,bool)),X4899),X4900))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X4898,bool),nat,finite_card(X4898),X4900)),hAPP(fun(X4898,bool),nat,finite_card(X4898),X4899)))
      | ti(fun(X4898,bool),X4899) = ti(fun(X4898,bool),X4900) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_281_card__seteq])]) ).

fof(i_0_1247,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_233_not__add__less1]) ).

fof(i_0_1248,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_234_not__add__less2]) ).

fof(i_0_1249,plain,
    ! [X1,X17,X40,X43] :
      ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43)))
     => ~ ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40))
         => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43)) ) ),
    inference(fof_simplification,[status(thm)],[fact_869_IntE]) ).

fof(i_0_1250,plain,
    ! [X5555,X5556,X5557,X5558] :
      ( ~ hBOOL(hAPP(fun(X5555,bool),bool,hAPP(fun(X5555,X5556),fun(fun(X5555,bool),bool),inj_on(X5555,X5556),X5558),top_top(fun(X5555,bool))))
      | hAPP(fun(X5556,bool),fun(X5555,bool),hAPP(fun(X5556,X5555),fun(fun(X5556,bool),fun(X5555,bool)),image(X5556,X5555),hAPP(fun(X5555,X5556),fun(X5556,X5555),hAPP(fun(X5555,bool),fun(fun(X5555,X5556),fun(X5556,X5555)),hilbert_inv_into(X5555,X5556),top_top(fun(X5555,bool))),X5558)),hAPP(fun(X5555,bool),fun(X5556,bool),hAPP(fun(X5555,X5556),fun(fun(X5555,bool),fun(X5556,bool)),image(X5555,X5556),X5558),X5557)) = ti(fun(X5555,bool),X5557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_506_image__inv__f__f])]) ).

fof(i_0_1251,plain,
    ! [X5551,X5552,X5553,X5554] :
      ( ~ hBOOL(hAPP(fun(X5551,bool),bool,hAPP(fun(X5551,X5552),fun(fun(X5551,bool),bool),inj_on(X5551,X5552),X5554),top_top(fun(X5551,bool))))
      | hAPP(fun(X5552,bool),fun(X5551,bool),hAPP(fun(X5552,X5551),fun(fun(X5552,bool),fun(X5551,bool)),image(X5552,X5551),hAPP(fun(X5551,X5552),fun(X5552,X5551),hAPP(fun(X5551,bool),fun(fun(X5551,X5552),fun(X5552,X5551)),hilbert_inv_into(X5551,X5552),top_top(fun(X5551,bool))),X5554)),hAPP(fun(X5551,bool),fun(X5552,bool),hAPP(fun(X5551,X5552),fun(fun(X5551,bool),fun(X5552,bool)),image(X5551,X5552),X5554),X5553)) = ti(fun(X5551,bool),X5553) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_505_inv__image__comp])]) ).

fof(i_0_1252,plain,
    ! [X1,X40] :
      ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = 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)),X40) )
      & ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
       => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ) ),
    inference(fof_simplification,[status(thm)],[fact_455_card__def]) ).

fof(i_0_1253,plain,
    ! [X5774,X5775,X5776,X5777] :
      ( ~ hBOOL(hAPP(fun(X5774,bool),bool,hAPP(fun(X5774,X5775),fun(fun(X5774,bool),bool),inj_on(X5774,X5775),X5776),X5777))
      | hAPP(fun(X5775,bool),fun(X5774,bool),hAPP(fun(X5775,X5774),fun(fun(X5775,bool),fun(X5774,bool)),image(X5775,X5774),hAPP(fun(X5774,X5775),fun(X5775,X5774),hAPP(fun(X5774,bool),fun(fun(X5774,X5775),fun(X5775,X5774)),the_inv_into(X5774,X5775),X5777),X5776)),hAPP(fun(X5774,bool),fun(X5775,bool),hAPP(fun(X5774,X5775),fun(fun(X5774,bool),fun(X5775,bool)),image(X5774,X5775),X5776),X5777)) = ti(fun(X5774,bool),X5777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_557_the__inv__into__onto])]) ).

fof(i_0_1254,plain,
    ! [X5637,X5638,X5641,X5642,X5643,X5644] :
      ( ( ~ hBOOL(hAPP(fun(X5637,bool),bool,finite_finite_1(X5637),X5638))
        | ti(fun(X5637,bool),X5638) = hAPP(fun(nat,bool),fun(X5637,bool),hAPP(fun(nat,X5637),fun(fun(nat,bool),fun(X5637,bool)),image(nat,X5637),esk119_2(X5637,X5638)),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)),esk118_2(X5637,X5638)))) )
      & ( ti(fun(X5641,bool),X5642) != hAPP(fun(nat,bool),fun(X5641,bool),hAPP(fun(nat,X5641),fun(fun(nat,bool),fun(X5641,bool)),image(nat,X5641),X5644),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)),X5643)))
        | hBOOL(hAPP(fun(X5641,bool),bool,finite_finite_1(X5641),X5642)) ) ),
    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_522_finite__conv__nat__seg__image])])])])]) ).

fof(i_0_1255,plain,
    ! [X5604,X5605,X5606,X5607] :
      ( ti(fun(X5604,bool),X5605) != hAPP(fun(nat,bool),fun(X5604,bool),hAPP(fun(nat,X5604),fun(fun(nat,bool),fun(X5604,bool)),image(nat,X5604),X5606),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)),X5607)))
      | hBOOL(hAPP(fun(X5604,bool),bool,finite_finite_1(X5604),X5605)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_516_nat__seg__image__imp__finite])]) ).

fof(i_0_1256,plain,
    ! [X5627,X5628,X5629,X5630] :
      ( ~ hBOOL(hAPP(fun(X5627,bool),bool,hAPP(X5627,fun(fun(X5627,bool),bool),member(X5627),X5629),hAPP(fun(X5628,bool),fun(X5627,bool),hAPP(fun(X5628,X5627),fun(fun(X5628,bool),fun(X5627,bool)),image(X5628,X5627),X5630),top_top(fun(X5628,bool)))))
      | ti(X5627,X5629) = hAPP(X5628,X5627,X5630,esk116_4(X5627,X5628,X5629,X5630)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_520_rangeE])])]) ).

fof(i_0_1257,plain,
    ! [X5477,X5478,X5479,X5480,X5481,X5482,X5483] :
      ( ( hAPP(fun(X5477,bool),fun(X5478,bool),hAPP(fun(X5477,X5478),fun(fun(X5477,bool),fun(X5478,bool)),image(X5477,X5478),X5479),top_top(fun(X5477,bool))) != top_top(fun(X5478,bool))
        | hAPP(X5477,X5478,X5479,hAPP(X5478,X5477,hAPP(fun(X5477,X5478),fun(X5478,X5477),hAPP(fun(X5477,bool),fun(fun(X5477,X5478),fun(X5478,X5477)),hilbert_inv_into(X5477,X5478),top_top(fun(X5477,bool))),X5479),X5480)) = ti(X5478,X5480) )
      & ( hAPP(X5481,X5482,X5483,hAPP(X5482,X5481,hAPP(fun(X5481,X5482),fun(X5482,X5481),hAPP(fun(X5481,bool),fun(fun(X5481,X5482),fun(X5482,X5481)),hilbert_inv_into(X5481,X5482),top_top(fun(X5481,bool))),X5483),esk106_3(X5481,X5482,X5483))) != ti(X5482,esk106_3(X5481,X5482,X5483))
        | hAPP(fun(X5481,bool),fun(X5482,bool),hAPP(fun(X5481,X5482),fun(fun(X5481,bool),fun(X5482,bool)),image(X5481,X5482),X5483),top_top(fun(X5481,bool))) = top_top(fun(X5482,bool)) ) ),
    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_487_surj__iff__all])])])])]) ).

fof(i_0_1258,plain,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X40] :
          ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
           => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),plus_plus(X2)),X39),zero_zero(X2)),X40) )
          & ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
           => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_970_setsum_OF__eq]) ).

fof(i_0_1259,plain,
    ! [X4172,X4173] :
      ( ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X4172,X4173)),arrow_1568854078le_Lin))
        | ti(arrow_2142409994le_alt,X4172) = ti(arrow_2142409994le_alt,X4173) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4172),X4173)),esk27_2(X4172,X4173)))
        | ti(arrow_2142409994le_alt,X4172) = ti(arrow_2142409994le_alt,X4173) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_complete__Lin])])])]) ).

fof(i_0_1260,plain,
    ! [X4347,X4348,X4349,X4350,X4351,X4352] :
      ( ( hAPP(X4347,X4348,X4351,X4350) != hAPP(X4347,X4348,X4351,X4349)
        | ti(X4347,X4350) = ti(X4347,X4349)
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(X4347,fun(fun(X4347,bool),bool),member(X4347),X4349),X4352))
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(X4347,fun(fun(X4347,bool),bool),member(X4347),X4350),X4352))
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(fun(X4347,X4348),fun(fun(X4347,bool),bool),inj_on(X4347,X4348),X4351),X4352)) )
      & ( ti(X4347,X4350) != ti(X4347,X4349)
        | hAPP(X4347,X4348,X4351,X4350) = hAPP(X4347,X4348,X4351,X4349)
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(X4347,fun(fun(X4347,bool),bool),member(X4347),X4349),X4352))
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(X4347,fun(fun(X4347,bool),bool),member(X4347),X4350),X4352))
        | ~ hBOOL(hAPP(fun(X4347,bool),bool,hAPP(fun(X4347,X4348),fun(fun(X4347,bool),bool),inj_on(X4347,X4348),X4351),X4352)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_inj__on__iff])])]) ).

fof(i_0_1261,plain,
    ! [X4353,X4354,X4355,X4356,X4357,X4358] :
      ( ~ hBOOL(hAPP(fun(X4353,bool),bool,hAPP(fun(X4353,X4354),fun(fun(X4353,bool),bool),inj_on(X4353,X4354),X4357),X4358))
      | hAPP(X4353,X4354,X4357,X4355) != hAPP(X4353,X4354,X4357,X4356)
      | ~ hBOOL(hAPP(fun(X4353,bool),bool,hAPP(X4353,fun(fun(X4353,bool),bool),member(X4353),X4355),X4358))
      | ~ hBOOL(hAPP(fun(X4353,bool),bool,hAPP(X4353,fun(fun(X4353,bool),bool),member(X4353),X4356),X4358))
      | ti(X4353,X4355) = ti(X4353,X4356) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_inj__onD])]) ).

fof(i_0_1262,plain,
    ! [X4341,X4342,X4343,X4344,X4345,X4346] :
      ( ~ hBOOL(hAPP(fun(X4341,bool),bool,hAPP(fun(X4341,X4342),fun(fun(X4341,bool),bool),inj_on(X4341,X4342),X4345),X4346))
      | ti(X4341,X4343) = ti(X4341,X4344)
      | ~ hBOOL(hAPP(fun(X4341,bool),bool,hAPP(X4341,fun(fun(X4341,bool),bool),member(X4341),X4343),X4346))
      | ~ hBOOL(hAPP(fun(X4341,bool),bool,hAPP(X4341,fun(fun(X4341,bool),bool),member(X4341),X4344),X4346))
      | hAPP(X4341,X4342,X4345,X4343) != hAPP(X4341,X4342,X4345,X4344) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_inj__on__contraD])]) ).

fof(i_0_1263,plain,
    ! [X4329,X4330,X4331,X4332,X4333,X4334,X4335,X4336,X4337,X4338] :
      ( ( ~ hBOOL(hAPP(fun(X4329,bool),bool,hAPP(fun(X4329,X4330),fun(fun(X4329,bool),bool),inj_on(X4329,X4330),X4331),X4332))
        | ~ hBOOL(hAPP(fun(X4329,bool),bool,hAPP(X4329,fun(fun(X4329,bool),bool),member(X4329),X4333),X4332))
        | ~ hBOOL(hAPP(fun(X4329,bool),bool,hAPP(X4329,fun(fun(X4329,bool),bool),member(X4329),X4334),X4332))
        | hAPP(X4329,X4330,X4331,X4333) != hAPP(X4329,X4330,X4331,X4334)
        | ti(X4329,X4333) = ti(X4329,X4334) )
      & ( hBOOL(hAPP(fun(X4335,bool),bool,hAPP(X4335,fun(fun(X4335,bool),bool),member(X4335),esk31_4(X4335,X4336,X4337,X4338)),X4338))
        | hBOOL(hAPP(fun(X4335,bool),bool,hAPP(fun(X4335,X4336),fun(fun(X4335,bool),bool),inj_on(X4335,X4336),X4337),X4338)) )
      & ( hBOOL(hAPP(fun(X4335,bool),bool,hAPP(X4335,fun(fun(X4335,bool),bool),member(X4335),esk32_4(X4335,X4336,X4337,X4338)),X4338))
        | hBOOL(hAPP(fun(X4335,bool),bool,hAPP(fun(X4335,X4336),fun(fun(X4335,bool),bool),inj_on(X4335,X4336),X4337),X4338)) )
      & ( hAPP(X4335,X4336,X4337,esk31_4(X4335,X4336,X4337,X4338)) = hAPP(X4335,X4336,X4337,esk32_4(X4335,X4336,X4337,X4338))
        | hBOOL(hAPP(fun(X4335,bool),bool,hAPP(fun(X4335,X4336),fun(fun(X4335,bool),bool),inj_on(X4335,X4336),X4337),X4338)) )
      & ( ti(X4335,esk31_4(X4335,X4336,X4337,X4338)) != ti(X4335,esk32_4(X4335,X4336,X4337,X4338))
        | hBOOL(hAPP(fun(X4335,bool),bool,hAPP(fun(X4335,X4336),fun(fun(X4335,bool),bool),inj_on(X4335,X4336),X4337),X4338)) ) ),
    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_135_inj__on__def])])])])])]) ).

fof(i_0_1264,plain,
    ! [X5326,X5327,X5328,X5329,X5330,X5331] :
      ( ti(X5326,X5329) != hAPP(X5327,X5326,X5330,X5331)
      | ~ hBOOL(hAPP(fun(X5327,bool),bool,hAPP(X5327,fun(fun(X5327,bool),bool),member(X5327),X5331),X5328))
      | hBOOL(hAPP(fun(X5326,bool),bool,hAPP(X5326,fun(fun(X5326,bool),bool),member(X5326),X5329),hAPP(fun(X5327,bool),fun(X5326,bool),hAPP(fun(X5327,X5326),fun(fun(X5327,bool),fun(X5326,bool)),image(X5327,X5326),X5330),X5328))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_458_image__eqI])]) ).

fof(i_0_1265,plain,
    ! [X5390,X5391,X5392,X5393,X5394,X5395] :
      ( ~ hBOOL(hAPP(fun(X5391,bool),bool,hAPP(X5391,fun(fun(X5391,bool),bool),member(X5391),X5394),X5395))
      | ti(X5390,X5392) != hAPP(X5391,X5390,X5393,X5394)
      | hBOOL(hAPP(fun(X5390,bool),bool,hAPP(X5390,fun(fun(X5390,bool),bool),member(X5390),X5392),hAPP(fun(X5391,bool),fun(X5390,bool),hAPP(fun(X5391,X5390),fun(fun(X5391,bool),fun(X5390,bool)),image(X5391,X5390),X5393),X5395))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_rev__image__eqI])]) ).

fof(i_0_1266,plain,
    ~ ! [X32] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),X32))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X32),arrow_1568854078le_Lin)) ),
    inference(fof_simplification,[status(thm)],[fact_44__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_]) ).

fof(i_0_1267,plain,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X31),arrow_1568854078le_Lin)) ),
    inference(fof_simplification,[status(thm)],[fact_43__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_]) ).

fof(i_0_1268,plain,
    ! [X4393,X4394,X4395,X4396,X4397,X4398] :
      ( ~ hBOOL(hAPP(fun(X4393,bool),bool,hAPP(fun(X4393,X4394),fun(fun(X4393,bool),bool),inj_on(X4393,X4394),X4397),X4398))
      | ~ hBOOL(hAPP(fun(X4393,bool),bool,hAPP(X4393,fun(fun(X4393,bool),bool),member(X4393),X4396),X4398))
      | hAPP(X4393,X4394,X4397,X4396) != ti(X4394,X4395)
      | hAPP(X4394,X4393,hAPP(fun(X4393,X4394),fun(X4394,X4393),hAPP(fun(X4393,bool),fun(fun(X4393,X4394),fun(X4394,X4393)),hilbert_inv_into(X4393,X4394),X4398),X4397),X4395) = ti(X4393,X4396) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_inv__into__f__eq])]) ).

fof(i_0_1269,plain,
    ! [X5753,X5754,X5755,X5756,X5757,X5758] :
      ( ~ hBOOL(hAPP(fun(X5753,bool),bool,hAPP(fun(X5753,X5754),fun(fun(X5753,bool),bool),inj_on(X5753,X5754),X5757),X5758))
      | hAPP(X5753,X5754,X5757,X5755) != ti(X5754,X5756)
      | ~ hBOOL(hAPP(fun(X5753,bool),bool,hAPP(X5753,fun(fun(X5753,bool),bool),member(X5753),X5755),X5758))
      | hAPP(X5754,X5753,hAPP(fun(X5753,X5754),fun(X5754,X5753),hAPP(fun(X5753,bool),fun(fun(X5753,X5754),fun(X5754,X5753)),the_inv_into(X5753,X5754),X5758),X5757),X5756) = ti(X5753,X5755) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_552_the__inv__into__f__eq])]) ).

fof(i_0_1270,plain,
    ! [X1,X40,X17,X43] :
      ( ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),X40)) )
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X17),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43))) ),
    inference(fof_simplification,[status(thm)],[fact_777_UnCI]) ).

fof(i_0_1271,plain,
    ! [X4388,X4389,X4390,X4391,X4392] :
      ( ~ hBOOL(hAPP(fun(X4388,bool),bool,hAPP(fun(X4388,X4389),fun(fun(X4388,bool),bool),inj_on(X4388,X4389),X4391),X4392))
      | ~ hBOOL(hAPP(fun(X4388,bool),bool,hAPP(X4388,fun(fun(X4388,bool),bool),member(X4388),X4390),X4392))
      | hAPP(X4389,X4388,hAPP(fun(X4388,X4389),fun(X4389,X4388),hAPP(fun(X4388,bool),fun(fun(X4388,X4389),fun(X4389,X4388)),hilbert_inv_into(X4388,X4389),X4392),X4391),hAPP(X4388,X4389,X4391,X4390)) = ti(X4388,X4390) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_inv__into__f__f])]) ).

fof(i_0_1272,plain,
    ! [X5759,X5760,X5761,X5762,X5763] :
      ( ~ hBOOL(hAPP(fun(X5759,bool),bool,hAPP(fun(X5759,X5760),fun(fun(X5759,bool),bool),inj_on(X5759,X5760),X5762),X5763))
      | ~ hBOOL(hAPP(fun(X5759,bool),bool,hAPP(X5759,fun(fun(X5759,bool),bool),member(X5759),X5761),X5763))
      | hAPP(X5760,X5759,hAPP(fun(X5759,X5760),fun(X5760,X5759),hAPP(fun(X5759,bool),fun(fun(X5759,X5760),fun(X5760,X5759)),the_inv_into(X5759,X5760),X5763),X5762),hAPP(X5759,X5760,X5762,X5761)) = ti(X5759,X5761) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_553_the__inv__into__f__f])]) ).

fof(i_0_1273,plain,
    ! [X1] :
      ( semilattice_inf(X1)
     => ! [X34,X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X21),X22)))
         => ~ ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X21))
             => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_920_le__infE]) ).

fof(i_0_1274,plain,
    ! [X6126,X6127,X6128,X6129,X6130,X6131] :
      ( ~ semiri456707255roduct(X6126)
      | ti(X6126,X6131) = zero_zero(X6126)
      | ti(X6126,X6129) != ti(X6126,X6130)
      | ti(X6126,X6127) = ti(X6126,X6128)
      | hAPP(X6126,X6126,hAPP(X6126,fun(X6126,X6126),plus_plus(X6126),X6129),hAPP(X6126,X6126,hAPP(X6126,fun(X6126,X6126),times_times(X6126),X6131),X6127)) != hAPP(X6126,X6126,hAPP(X6126,fun(X6126,X6126),plus_plus(X6126),X6130),hAPP(X6126,X6126,hAPP(X6126,fun(X6126,X6126),times_times(X6126),X6131),X6128)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_654_add__scale__eq__noteq])])]) ).

fof(i_0_1275,plain,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6))
     => ( ~ hBOOL(hAPP(X1,bool,X40,X6))
       => hBOOL(hAPP(X1,bool,X43,X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_775_sup1E]) ).

fof(i_0_1276,plain,
    ! [X6123,X6124,X6125] :
      ( ( ti(X6123,X6124) = zero_zero(X6123)
        | hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),plus_plus(X6123),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6124),X6124)),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6125),X6125)) != zero_zero(X6123)
        | ~ linord581940658strict(X6123) )
      & ( ti(X6123,X6125) = zero_zero(X6123)
        | hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),plus_plus(X6123),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6124),X6124)),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6125),X6125)) != zero_zero(X6123)
        | ~ linord581940658strict(X6123) )
      & ( ti(X6123,X6124) != zero_zero(X6123)
        | ti(X6123,X6125) != zero_zero(X6123)
        | hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),plus_plus(X6123),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6124),X6124)),hAPP(X6123,X6123,hAPP(X6123,fun(X6123,X6123),times_times(X6123),X6125),X6125)) = zero_zero(X6123)
        | ~ linord581940658strict(X6123) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_653_sum__squares__eq__zero__iff])])])]) ).

fof(i_0_1277,plain,
    ! [X4405,X4406,X4407,X4408] :
      ( ~ hBOOL(hAPP(fun(X4405,bool),bool,hAPP(fun(X4405,X4406),fun(fun(X4405,bool),bool),inj_on(X4405,X4406),X4408),top_top(fun(X4405,bool))))
      | hAPP(X4405,X4406,X4408,hAPP(X4406,X4405,X4407,esk34_4(X4405,X4406,X4407,X4408))) != ti(X4406,esk34_4(X4405,X4406,X4407,X4408))
      | hAPP(fun(X4405,X4406),fun(X4406,X4405),hAPP(fun(X4405,bool),fun(fun(X4405,X4406),fun(X4406,X4405)),hilbert_inv_into(X4405,X4406),top_top(fun(X4405,bool))),X4408) = ti(fun(X4406,X4405),X4407) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_inj__imp__inv__eq])])]) ).

fof(i_0_1278,plain,
    ! [X3840,X3841] : ti(fun(fun(X3840,fun(X3840,X3840)),fun(X3840,fun(fun(fun(X3841,X3840),fun(fun(X3841,bool),X3840)),bool))),finite_folding_image(X3840,X3841)) = finite_folding_image(X3840,X3841),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image_res]) ).

fof(i_0_1279,plain,
    ! [X1,X40,X43,X6] :
      ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X40),X43),X6))
     => ~ ( hBOOL(hAPP(X1,bool,X40,X6))
         => ~ hBOOL(hAPP(X1,bool,X43,X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_868_inf1E]) ).

fof(i_0_1280,plain,
    ! [X5406,X5407,X5408,X5409,X5410] :
      ( ( ti(X5406,X5409) = ti(X5406,X5407)
        | hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5409),X5410) != hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5407),X5408)
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5407),X5408))
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5409),X5410))
        | ~ linorder(X5406) )
      & ( ti(X5406,X5410) = ti(X5406,X5408)
        | hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5409),X5410) != hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5407),X5408)
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5407),X5408))
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5409),X5410))
        | ~ linorder(X5406) )
      & ( ti(X5406,X5409) != ti(X5406,X5407)
        | ti(X5406,X5410) != ti(X5406,X5408)
        | hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5409),X5410) = hAPP(X5406,fun(X5406,bool),hAPP(X5406,fun(X5406,fun(X5406,bool)),ord_atLeastLessThan(X5406),X5407),X5408)
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5407),X5408))
        | ~ hBOOL(hAPP(X5406,bool,hAPP(X5406,fun(X5406,bool),ord_less(X5406),X5409),X5410))
        | ~ linorder(X5406) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_atLeastLessThan__eq__iff])])])]) ).

fof(i_0_1281,plain,
    ! [X5401,X5402,X5403,X5404,X5405] :
      ( ~ linorder(X5401)
      | hAPP(X5401,fun(X5401,bool),hAPP(X5401,fun(X5401,fun(X5401,bool)),ord_atLeastLessThan(X5401),X5402),X5403) != hAPP(X5401,fun(X5401,bool),hAPP(X5401,fun(X5401,fun(X5401,bool)),ord_atLeastLessThan(X5401),X5404),X5405)
      | ~ hBOOL(hAPP(X5401,bool,hAPP(X5401,fun(X5401,bool),ord_less(X5401),X5402),X5403))
      | ~ hBOOL(hAPP(X5401,bool,hAPP(X5401,fun(X5401,bool),ord_less(X5401),X5404),X5405))
      | ti(X5401,X5402) = ti(X5401,X5404) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_472_atLeastLessThan__inj_I1_J])])]) ).

fof(i_0_1282,plain,
    ! [X5396,X5397,X5398,X5399,X5400] :
      ( ~ linorder(X5396)
      | hAPP(X5396,fun(X5396,bool),hAPP(X5396,fun(X5396,fun(X5396,bool)),ord_atLeastLessThan(X5396),X5397),X5398) != hAPP(X5396,fun(X5396,bool),hAPP(X5396,fun(X5396,fun(X5396,bool)),ord_atLeastLessThan(X5396),X5399),X5400)
      | ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less(X5396),X5397),X5398))
      | ~ hBOOL(hAPP(X5396,bool,hAPP(X5396,fun(X5396,bool),ord_less(X5396),X5399),X5400))
      | ti(X5396,X5398) = ti(X5396,X5400) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_atLeastLessThan__inj_I2_J])])]) ).

fof(i_0_1283,plain,
    ! [X6175,X6176,X6177,X6178] :
      ( ~ hBOOL(hAPP(fun(fun(X6175,X6176),bool),bool,hAPP(fun(X6175,X6176),fun(fun(fun(X6175,X6176),bool),bool),member(fun(X6175,X6176)),X6177),hAPP(fun(X6175,bool),fun(fun(X6175,X6176),bool),extensional(X6175,X6176),X6178)))
      | hAPP(fun(X6175,bool),fun(X6175,X6176),hAPP(fun(X6175,X6176),fun(fun(X6175,bool),fun(X6175,X6176)),restrict(X6175,X6176),X6177),X6178) = ti(fun(X6175,X6176),X6177) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_671_extensional__restrict])]) ).

fof(i_0_1284,plain,
    ! [X54,X30] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X30)),X54)) ),
    inference(fof_simplification,[status(thm)],[fact_405_not__less__eq__eq]) ).

fof(i_0_1285,plain,
    ! [X5473,X5474,X5475,X5476] :
      ( hAPP(fun(X5473,bool),fun(X5474,bool),hAPP(fun(X5473,X5474),fun(fun(X5473,bool),fun(X5474,bool)),image(X5473,X5474),X5476),top_top(fun(X5473,bool))) != top_top(fun(X5474,bool))
      | hAPP(X5473,X5474,X5476,hAPP(X5474,X5473,hAPP(fun(X5473,X5474),fun(X5474,X5473),hAPP(fun(X5473,bool),fun(fun(X5473,X5474),fun(X5474,X5473)),hilbert_inv_into(X5473,X5474),top_top(fun(X5473,bool))),X5476),X5475)) = ti(X5474,X5475) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_486_surj__f__inv__f])]) ).

fof(i_0_1286,plain,
    ! [X5645,X5646] :
      ( ( ti(fun(X5645,bool),X5646) = hAPP(fun(nat,bool),fun(X5645,bool),hAPP(fun(nat,X5645),fun(fun(nat,bool),fun(X5645,bool)),image(nat,X5645),esk121_2(X5645,X5646)),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)),esk120_2(X5645,X5646))))
        | ~ hBOOL(hAPP(fun(X5645,bool),bool,finite_finite_1(X5645),X5646)) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X5645),fun(fun(nat,bool),bool),inj_on(nat,X5645),esk121_2(X5645,X5646)),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)),esk120_2(X5645,X5646)))))
        | ~ hBOOL(hAPP(fun(X5645,bool),bool,finite_finite_1(X5645),X5646)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_523_finite__imp__nat__seg__image__inj__on])])])]) ).

fof(i_0_1287,plain,
    ! [X3842,X3843] : ti(fun(fun(X3842,fun(X3842,X3842)),fun(X3842,fun(fun(X3843,X3842),fun(fun(fun(X3843,bool),X3842),bool)))),finite908156982e_idem(X3842,X3843)) = finite908156982e_idem(X3842,X3843),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple__idem_res]) ).

fof(i_0_1288,plain,
    ! [X1,X2] :
      ( ord(X2)
     => ! [X38,X39] :
          ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less(fun(X1,X2)),X38),X39))
        <=> ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X38),X39))
            & ~ hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X39),X38)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_159_less__fun__def]) ).

fof(i_0_1289,plain,
    ! [X5454,X5455,X5456,X5457,X5458] :
      ( ( hAPP(fun(X5454,bool),fun(X5455,bool),hAPP(fun(X5454,X5455),fun(fun(X5454,bool),fun(X5455,bool)),image(X5454,X5455),X5458),X5456) != hAPP(fun(X5454,bool),fun(X5455,bool),hAPP(fun(X5454,X5455),fun(fun(X5454,bool),fun(X5455,bool)),image(X5454,X5455),X5458),X5457)
        | ti(fun(X5454,bool),X5456) = ti(fun(X5454,bool),X5457)
        | ~ hBOOL(hAPP(fun(X5454,bool),bool,hAPP(fun(X5454,X5455),fun(fun(X5454,bool),bool),inj_on(X5454,X5455),X5458),top_top(fun(X5454,bool)))) )
      & ( ti(fun(X5454,bool),X5456) != ti(fun(X5454,bool),X5457)
        | hAPP(fun(X5454,bool),fun(X5455,bool),hAPP(fun(X5454,X5455),fun(fun(X5454,bool),fun(X5455,bool)),image(X5454,X5455),X5458),X5456) = hAPP(fun(X5454,bool),fun(X5455,bool),hAPP(fun(X5454,X5455),fun(fun(X5454,bool),fun(X5455,bool)),image(X5454,X5455),X5458),X5457)
        | ~ hBOOL(hAPP(fun(X5454,bool),bool,hAPP(fun(X5454,X5455),fun(fun(X5454,bool),bool),inj_on(X5454,X5455),X5458),top_top(fun(X5454,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_482_inj__image__eq__iff])])]) ).

fof(i_0_1290,plain,
    ! [X5591,X5592,X5593,X5594] :
      ( hAPP(fun(X5591,bool),fun(X5592,bool),hAPP(fun(X5591,X5592),fun(fun(X5591,bool),fun(X5592,bool)),image(X5591,X5592),X5594),top_top(fun(X5591,bool))) != top_top(fun(X5592,bool))
      | hAPP(X5592,X5591,X5593,hAPP(X5591,X5592,X5594,esk110_4(X5591,X5592,X5593,X5594))) != ti(X5591,esk110_4(X5591,X5592,X5593,X5594))
      | hAPP(fun(X5591,X5592),fun(X5592,X5591),hAPP(fun(X5591,bool),fun(fun(X5591,X5592),fun(X5592,X5591)),hilbert_inv_into(X5591,X5592),top_top(fun(X5591,bool))),X5594) = ti(fun(X5592,X5591),X5593) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_513_surj__imp__inv__eq])])]) ).

fof(i_0_1291,plain,
    ! [X7526,X7527,X7528,X7530,X7531] :
      ( ( hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),esk175_3(X7526,X7527,X7528)),X7528))
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) )
      & ( hAPP(X7526,nat,X7527,esk175_3(X7526,X7527,X7528)) = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) )
      & ( ~ hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),X7530),X7528))
        | ti(X7526,esk175_3(X7526,X7527,X7528)) = ti(X7526,X7530)
        | hAPP(X7526,nat,X7527,X7530) = zero_zero(nat)
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) )
      & ( hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),esk176_4(X7526,X7527,X7528,X7531)),X7528))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),X7531),X7528))
        | hAPP(X7526,nat,X7527,X7531) != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) )
      & ( ti(X7526,X7531) != ti(X7526,esk176_4(X7526,X7527,X7528,X7531))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),X7531),X7528))
        | hAPP(X7526,nat,X7527,X7531) != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) )
      & ( hAPP(X7526,nat,X7527,esk176_4(X7526,X7527,X7528,X7531)) != zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,hAPP(X7526,fun(fun(X7526,bool),bool),member(X7526),X7531),X7528))
        | hAPP(X7526,nat,X7527,X7531) != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(fun(X7526,bool),nat,hAPP(fun(X7526,nat),fun(fun(X7526,bool),nat),big_co1399186613setsum(X7526,nat),X7527),X7528) = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ hBOOL(hAPP(fun(X7526,bool),bool,finite_finite_1(X7526),X7528)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_992_setsum__eq__Suc0__iff])])])])]) ).

fof(i_0_1292,plain,
    ! [X5360,X5361,X5362,X5363,X5364] :
      ( ti(X5360,X5362) != hAPP(X5361,X5360,X5363,X5364)
      | hBOOL(hAPP(fun(X5360,bool),bool,hAPP(X5360,fun(fun(X5360,bool),bool),member(X5360),X5362),hAPP(fun(X5361,bool),fun(X5360,bool),hAPP(fun(X5361,X5360),fun(fun(X5361,bool),fun(X5360,bool)),image(X5361,X5360),X5363),top_top(fun(X5361,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_range__eqI])]) ).

fof(i_0_1293,plain,
    ! [X4684,X4685,X4686] :
      ( ( hBOOL(hAPP(fun(X4684,bool),bool,hAPP(fun(X4684,bool),fun(fun(X4684,bool),bool),ord_less_eq(fun(X4684,bool)),X4685),X4686))
        | ti(fun(X4684,bool),X4685) != ti(fun(X4684,bool),X4686) )
      & ( hBOOL(hAPP(fun(X4684,bool),bool,hAPP(fun(X4684,bool),fun(fun(X4684,bool),bool),ord_less_eq(fun(X4684,bool)),X4686),X4685))
        | ti(fun(X4684,bool),X4685) != ti(fun(X4684,bool),X4686) )
      & ( ~ hBOOL(hAPP(fun(X4684,bool),bool,hAPP(fun(X4684,bool),fun(fun(X4684,bool),bool),ord_less_eq(fun(X4684,bool)),X4685),X4686))
        | ~ hBOOL(hAPP(fun(X4684,bool),bool,hAPP(fun(X4684,bool),fun(fun(X4684,bool),bool),ord_less_eq(fun(X4684,bool)),X4686),X4685))
        | ti(fun(X4684,bool),X4685) = ti(fun(X4684,bool),X4686) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_set__eq__subset])])]) ).

fof(i_0_1294,plain,
    ! [X4615,X4616,X4617] :
      ( ~ hBOOL(hAPP(fun(X4615,bool),bool,hAPP(fun(X4615,bool),fun(fun(X4615,bool),bool),ord_less_eq(fun(X4615,bool)),X4616),X4617))
      | ~ hBOOL(hAPP(fun(X4615,bool),bool,hAPP(fun(X4615,bool),fun(fun(X4615,bool),bool),ord_less_eq(fun(X4615,bool)),X4617),X4616))
      | ti(fun(X4615,bool),X4616) = ti(fun(X4615,bool),X4617) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_equalityI])]) ).

fof(i_0_1295,plain,
    ! [X4157,X4158,X4159,X4160,X4161] :
      ( ~ hBOOL(hAPP(fun(X4157,bool),bool,hAPP(fun(X4157,X4158),fun(fun(X4157,bool),bool),inj_on(X4157,X4158),X4161),top_top(fun(X4157,bool))))
      | hAPP(X4157,X4158,X4161,X4159) != ti(X4158,X4160)
      | hAPP(X4158,X4157,hAPP(fun(X4157,X4158),fun(X4158,X4157),hAPP(fun(X4157,bool),fun(fun(X4157,X4158),fun(X4158,X4157)),hilbert_inv_into(X4157,X4158),top_top(fun(X4157,bool))),X4161),X4160) = ti(X4157,X4159) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_inv__f__eq])]) ).

fof(i_0_1296,plain,
    ! [X4162,X4163,X4164,X4165] :
      ( ~ hBOOL(hAPP(fun(X4162,bool),bool,hAPP(fun(X4162,X4163),fun(fun(X4162,bool),bool),inj_on(X4162,X4163),X4165),top_top(fun(X4162,bool))))
      | hAPP(X4163,X4162,hAPP(fun(X4162,X4163),fun(X4163,X4162),hAPP(fun(X4162,bool),fun(fun(X4162,X4163),fun(X4163,X4162)),hilbert_inv_into(X4162,X4163),top_top(fun(X4162,bool))),X4165),hAPP(X4162,X4163,X4165,X4164)) = ti(X4162,X4164) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_inv__f__f])]) ).

fof(i_0_1297,plain,
    ! [X5766,X5767,X5768,X5769] :
      ( ~ hBOOL(hAPP(fun(X5766,bool),bool,hAPP(fun(X5766,X5767),fun(fun(X5766,bool),bool),inj_on(X5766,X5767),X5769),top_top(fun(X5766,bool))))
      | hAPP(X5767,X5766,hAPP(fun(X5766,X5767),fun(X5767,X5766),hAPP(fun(X5766,bool),fun(fun(X5766,X5767),fun(X5767,X5766)),the_inv_into(X5766,X5767),top_top(fun(X5766,bool))),X5769),hAPP(X5766,X5767,X5769,X5768)) = ti(X5766,X5768) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_555_the__inv__f__f])]) ).

fof(i_0_1298,plain,
    ! [X5060,X5061,X5062] :
      ( ( ti(X5060,X5062) = zero_zero(X5060)
        | hAPP(X5060,X5060,hAPP(X5060,fun(X5060,X5060),plus_plus(X5060),X5062),X5061) != zero_zero(X5060)
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5061))
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5062))
        | ~ ordere216010020id_add(X5060) )
      & ( ti(X5060,X5061) = zero_zero(X5060)
        | hAPP(X5060,X5060,hAPP(X5060,fun(X5060,X5060),plus_plus(X5060),X5062),X5061) != zero_zero(X5060)
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5061))
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5062))
        | ~ ordere216010020id_add(X5060) )
      & ( ti(X5060,X5062) != zero_zero(X5060)
        | ti(X5060,X5061) != zero_zero(X5060)
        | hAPP(X5060,X5060,hAPP(X5060,fun(X5060,X5060),plus_plus(X5060),X5062),X5061) = zero_zero(X5060)
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5061))
        | ~ hBOOL(hAPP(X5060,bool,hAPP(X5060,fun(X5060,bool),ord_less_eq(X5060),zero_zero(X5060)),X5062))
        | ~ ordere216010020id_add(X5060) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_add__nonneg__eq__0__iff])])])]) ).

fof(i_0_1299,plain,
    ! [X7533,X7534,X7535,X7537,X7538] :
      ( ( hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),esk177_3(X7533,X7534,X7535)),X7535))
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) != one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) )
      & ( hAPP(X7533,nat,X7534,esk177_3(X7533,X7534,X7535)) = one_one(nat)
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) != one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) )
      & ( ~ hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),X7537),X7535))
        | ti(X7533,esk177_3(X7533,X7534,X7535)) = ti(X7533,X7537)
        | hAPP(X7533,nat,X7534,X7537) = zero_zero(nat)
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) != one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) )
      & ( hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),esk178_4(X7533,X7534,X7535,X7538)),X7535))
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),X7538),X7535))
        | hAPP(X7533,nat,X7534,X7538) != one_one(nat)
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) = one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) )
      & ( ti(X7533,X7538) != ti(X7533,esk178_4(X7533,X7534,X7535,X7538))
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),X7538),X7535))
        | hAPP(X7533,nat,X7534,X7538) != one_one(nat)
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) = one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) )
      & ( hAPP(X7533,nat,X7534,esk178_4(X7533,X7534,X7535,X7538)) != zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,hAPP(X7533,fun(fun(X7533,bool),bool),member(X7533),X7538),X7535))
        | hAPP(X7533,nat,X7534,X7538) != one_one(nat)
        | hAPP(fun(X7533,bool),nat,hAPP(fun(X7533,nat),fun(fun(X7533,bool),nat),big_co1399186613setsum(X7533,nat),X7534),X7535) = one_one(nat)
        | ~ hBOOL(hAPP(fun(X7533,bool),bool,finite_finite_1(X7533),X7535)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_993_setsum__eq__1__iff])])])])]) ).

fof(i_0_1300,plain,
    ! [X54,X30] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X30))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54))) ),
    inference(fof_simplification,[status(thm)],[fact_396_not__less__eq]) ).

fof(i_0_1301,plain,
    ! [X4625,X4626,X4627] :
      ( ( ~ hBOOL(hAPP(fun(X4625,bool),bool,hAPP(fun(X4625,bool),fun(fun(X4625,bool),bool),ord_less_eq(fun(X4625,bool)),X4626),X4627))
        | hBOOL(hAPP(fun(X4625,bool),bool,hAPP(fun(X4625,bool),fun(fun(X4625,bool),bool),ord_less(fun(X4625,bool)),X4626),X4627))
        | ti(fun(X4625,bool),X4626) = ti(fun(X4625,bool),X4627) )
      & ( ~ hBOOL(hAPP(fun(X4625,bool),bool,hAPP(fun(X4625,bool),fun(fun(X4625,bool),bool),ord_less(fun(X4625,bool)),X4626),X4627))
        | hBOOL(hAPP(fun(X4625,bool),bool,hAPP(fun(X4625,bool),fun(fun(X4625,bool),bool),ord_less_eq(fun(X4625,bool)),X4626),X4627)) )
      & ( ti(fun(X4625,bool),X4626) != ti(fun(X4625,bool),X4627)
        | hBOOL(hAPP(fun(X4625,bool),bool,hAPP(fun(X4625,bool),fun(fun(X4625,bool),bool),ord_less_eq(fun(X4625,bool)),X4626),X4627)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_197_subset__iff__psubset__eq])])]) ).

fof(i_0_1302,plain,
    ! [X4622,X4623,X4624] :
      ( ( hBOOL(hAPP(fun(X4622,bool),bool,hAPP(fun(X4622,bool),fun(fun(X4622,bool),bool),ord_less_eq(fun(X4622,bool)),X4623),X4624))
        | ~ hBOOL(hAPP(fun(X4622,bool),bool,hAPP(fun(X4622,bool),fun(fun(X4622,bool),bool),ord_less(fun(X4622,bool)),X4623),X4624)) )
      & ( ti(fun(X4622,bool),X4623) != ti(fun(X4622,bool),X4624)
        | ~ hBOOL(hAPP(fun(X4622,bool),bool,hAPP(fun(X4622,bool),fun(fun(X4622,bool),bool),ord_less(fun(X4622,bool)),X4623),X4624)) )
      & ( ~ hBOOL(hAPP(fun(X4622,bool),bool,hAPP(fun(X4622,bool),fun(fun(X4622,bool),bool),ord_less_eq(fun(X4622,bool)),X4623),X4624))
        | ti(fun(X4622,bool),X4623) = ti(fun(X4622,bool),X4624)
        | hBOOL(hAPP(fun(X4622,bool),bool,hAPP(fun(X4622,bool),fun(fun(X4622,bool),bool),ord_less(fun(X4622,bool)),X4623),X4624)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_196_psubset__eq])])]) ).

fof(i_0_1303,plain,
    ! [X1,X40,X43,X6] :
      ( ( ~ hBOOL(hAPP(X1,bool,X43,X6))
       => hBOOL(hAPP(X1,bool,X40,X6)) )
     => hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X40),X43),X6)) ),
    inference(fof_simplification,[status(thm)],[fact_776_sup1CI]) ).

fof(i_0_1304,plain,
    ! [X4295,X4296,X4297] :
      ( ( hBOOL(hAPP(X4295,bool,hAPP(X4295,fun(X4295,bool),ord_less(X4295),X4296),X4297))
        | ti(X4295,X4296) = ti(X4295,X4297)
        | ~ hBOOL(hAPP(X4295,bool,hAPP(X4295,fun(X4295,bool),ord_less_eq(X4295),X4296),X4297))
        | ~ linorder(X4295) )
      & ( ti(X4295,X4296) != ti(X4295,X4297)
        | ~ hBOOL(hAPP(X4295,bool,hAPP(X4295,fun(X4295,bool),ord_less(X4295),X4296),X4297))
        | ~ hBOOL(hAPP(X4295,bool,hAPP(X4295,fun(X4295,bool),ord_less_eq(X4295),X4296),X4297))
        | ~ linorder(X4295) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1170])])])]) ).

fof(i_0_1305,plain,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),hAPP(nat,nat,suc,X51)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X49),X51))
       => X49 = hAPP(nat,nat,suc,X51) ) ),
    inference(fof_simplification,[status(thm)],[fact_401_le__SucE]) ).

fof(i_0_1306,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
            & ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_115_less__le__not__le]) ).

fof(i_0_1307,plain,
    ! [X30,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,X54)))
      <=> X30 = X54 ) ),
    inference(fof_simplification,[status(thm)],[fact_393_not__less__less__Suc__eq]) ).

fof(i_0_1308,plain,
    ! [X51,X49] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X49))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X49)))
       => X49 = X51 ) ),
    inference(fof_simplification,[status(thm)],[fact_392_less__antisym]) ).

fof(i_0_1309,plain,
    ! [X49,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),hAPP(nat,nat,suc,X51)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X49),X51))
       => X49 = X51 ) ),
    inference(fof_simplification,[status(thm)],[fact_388_less__SucE]) ).

fof(i_0_1310,plain,
    ! [X4242,X4243,X4244] :
      ( ( hBOOL(hAPP(X4242,bool,hAPP(X4242,fun(X4242,bool),ord_less_eq(X4242),X4243),X4244))
        | ti(X4242,X4243) != ti(X4242,X4244)
        | ~ order(X4242) )
      & ( hBOOL(hAPP(X4242,bool,hAPP(X4242,fun(X4242,bool),ord_less_eq(X4242),X4244),X4243))
        | ti(X4242,X4243) != ti(X4242,X4244)
        | ~ order(X4242) )
      & ( ~ hBOOL(hAPP(X4242,bool,hAPP(X4242,fun(X4242,bool),ord_less_eq(X4242),X4243),X4244))
        | ~ hBOOL(hAPP(X4242,bool,hAPP(X4242,fun(X4242,bool),ord_less_eq(X4242),X4244),X4243))
        | ti(X4242,X4243) = ti(X4242,X4244)
        | ~ order(X4242) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_108_order__eq__iff])])])]) ).

fof(i_0_1311,plain,
    ! [X4231,X4232,X4233] :
      ( ( ~ hBOOL(hAPP(X4231,bool,hAPP(X4231,fun(X4231,bool),ord_less_eq(X4231),X4233),X4232))
        | ti(X4231,X4233) = ti(X4231,X4232)
        | ~ hBOOL(hAPP(X4231,bool,hAPP(X4231,fun(X4231,bool),ord_less_eq(X4231),X4232),X4233))
        | ~ order(X4231) )
      & ( ti(X4231,X4233) != ti(X4231,X4232)
        | hBOOL(hAPP(X4231,bool,hAPP(X4231,fun(X4231,bool),ord_less_eq(X4231),X4233),X4232))
        | ~ hBOOL(hAPP(X4231,bool,hAPP(X4231,fun(X4231,bool),ord_less_eq(X4231),X4232),X4233))
        | ~ order(X4231) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_105_order__antisym__conv])])])]) ).

fof(i_0_1312,plain,
    ! [X4212,X4213,X4214] :
      ( ~ order(X4212)
      | ~ hBOOL(hAPP(X4212,bool,hAPP(X4212,fun(X4212,bool),ord_less_eq(X4212),X4213),X4214))
      | ~ hBOOL(hAPP(X4212,bool,hAPP(X4212,fun(X4212,bool),ord_less_eq(X4212),X4214),X4213))
      | ti(X4212,X4213) = ti(X4212,X4214) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_100_order__antisym])])]) ).

fof(i_0_1313,plain,
    ! [X4205,X4206,X4207] :
      ( ~ order(X4205)
      | ~ hBOOL(hAPP(X4205,bool,hAPP(X4205,fun(X4205,bool),ord_less_eq(X4205),X4206),X4207))
      | ~ hBOOL(hAPP(X4205,bool,hAPP(X4205,fun(X4205,bool),ord_less_eq(X4205),X4207),X4206))
      | ti(X4205,X4207) = ti(X4205,X4206) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_xt1_I5_J])])]) ).

fof(i_0_1314,plain,
    ! [X6458,X6459,X6460,X6461,X6462,X6463] : hAPP(X6458,X6459,hAPP(fun(X6458,X6460),fun(X6458,X6459),hAPP(fun(X6460,X6459),fun(fun(X6458,X6460),fun(X6458,X6459)),comp(X6460,X6459,X6458),hAPP(X6459,fun(X6460,X6459),combk(X6459,X6460),X6461)),X6462),X6463) = ti(X6459,X6461),
    inference(variable_rename,[status(thm)],[fact_733_K__record__comp]) ).

fof(i_0_1315,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X51)),
    inference(fof_simplification,[status(thm)],[fact_406_Suc__n__not__le__n]) ).

fof(i_0_1316,plain,
    ! [X30,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X30))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X30))
            & ! [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_367_ex__least__nat__less]) ).

fof(i_0_1317,plain,
    ! [X5670,X5671,X5672,X5673] :
      ( hAPP(X5670,X5671,X5672,hAPP(X5671,X5670,X5673,esk128_4(X5670,X5671,X5672,X5673))) != ti(X5671,esk128_4(X5670,X5671,X5672,X5673))
      | hAPP(fun(X5670,bool),fun(X5671,bool),hAPP(fun(X5670,X5671),fun(fun(X5670,bool),fun(X5671,bool)),image(X5670,X5671),X5672),top_top(fun(X5670,bool))) = top_top(fun(X5671,bool)) ),
    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_528_surjI])])])])]) ).

fof(i_0_1318,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_67_order__less__not__sym]) ).

fof(i_0_1319,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_66_order__less__imp__not__less]) ).

fof(i_0_1320,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_62_order__less__asym_H]) ).

fof(i_0_1321,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X34,X35] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_54_order__less__asym]) ).

fof(i_0_1322,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_112_linorder__not__le]) ).

fof(i_0_1323,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X35,X34] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
    inference(fof_simplification,[status(thm)],[fact_122_leD]) ).

fof(i_0_1324,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
        <=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_111_linorder__not__less]) ).

fof(i_0_1325,plain,
    ! [X1] :
      ( order(X1)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X22),X21))
         => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[fact_61_xt1_I9_J]) ).

fof(i_0_1326,plain,
    ! [X4223,X4224,X4225,X4226] :
      ( ~ order(X4223)
      | ti(X4223,X4225) != ti(X4223,X4226)
      | ~ hBOOL(hAPP(X4223,bool,hAPP(X4223,fun(X4223,bool),ord_less_eq(X4223),X4224),X4226))
      | hBOOL(hAPP(X4223,bool,hAPP(X4223,fun(X4223,bool),ord_less_eq(X4223),X4224),X4225)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_xt1_I3_J])])]) ).

fof(i_0_1327,plain,
    ! [X4215,X4216,X4217,X4218] :
      ( ~ order(X4215)
      | ~ hBOOL(hAPP(X4215,bool,hAPP(X4215,fun(X4215,bool),ord_less_eq(X4215),X4217),X4218))
      | ti(X4215,X4217) != ti(X4215,X4216)
      | hBOOL(hAPP(X4215,bool,hAPP(X4215,fun(X4215,bool),ord_less_eq(X4215),X4216),X4218)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_xt1_I4_J])])]) ).

fof(i_0_1328,plain,
    ! [X4107,X4108,X4109] :
      ( ( hBOOL(hAPP(X4107,bool,hAPP(X4107,fun(X4107,bool),ord_less(X4107),X4109),X4108))
        | ti(X4107,X4109) = ti(X4107,X4108)
        | hBOOL(hAPP(X4107,bool,hAPP(X4107,fun(X4107,bool),ord_less(X4107),X4108),X4109))
        | ~ linorder(X4107) )
      & ( ti(X4107,X4109) != ti(X4107,X4108)
        | ~ hBOOL(hAPP(X4107,bool,hAPP(X4107,fun(X4107,bool),ord_less(X4107),X4109),X4108))
        | hBOOL(hAPP(X4107,bool,hAPP(X4107,fun(X4107,bool),ord_less(X4107),X4108),X4109))
        | ~ linorder(X4107) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1171])])])]) ).

fof(i_0_1329,plain,
    ! [X4071,X4072,X4073,X4074] :
      ( ~ order(X4071)
      | ti(X4071,X4073) != ti(X4071,X4074)
      | ~ hBOOL(hAPP(X4071,bool,hAPP(X4071,fun(X4071,bool),ord_less(X4071),X4072),X4074))
      | hBOOL(hAPP(X4071,bool,hAPP(X4071,fun(X4071,bool),ord_less(X4071),X4072),X4073)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_xt1_I1_J])])]) ).

fof(i_0_1330,plain,
    ! [X4063,X4064,X4065,X4066] :
      ( ~ order(X4063)
      | ~ hBOOL(hAPP(X4063,bool,hAPP(X4063,fun(X4063,bool),ord_less(X4063),X4065),X4066))
      | ti(X4063,X4065) != ti(X4063,X4064)
      | hBOOL(hAPP(X4063,bool,hAPP(X4063,fun(X4063,bool),ord_less(X4063),X4064),X4066)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_xt1_I2_J])])]) ).

fof(i_0_1331,plain,
    ! [X6715,X6716,X6717] :
      ( ~ hBOOL(hAPP(fun(X6715,bool),bool,hAPP(fun(X6715,bool),fun(fun(X6715,bool),bool),ord_less_eq(fun(X6715,bool)),X6716),X6717))
      | hAPP(fun(X6715,bool),fun(X6715,bool),hAPP(fun(X6715,bool),fun(fun(X6715,bool),fun(X6715,bool)),semilattice_sup_sup(fun(X6715,bool)),X6716),X6717) = ti(fun(X6715,bool),X6717) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_785_Un__absorb1])]) ).

fof(i_0_1332,plain,
    ! [X6712,X6713,X6714] :
      ( ( ~ hBOOL(hAPP(fun(X6712,bool),bool,hAPP(fun(X6712,bool),fun(fun(X6712,bool),bool),ord_less_eq(fun(X6712,bool)),X6713),X6714))
        | hAPP(fun(X6712,bool),fun(X6712,bool),hAPP(fun(X6712,bool),fun(fun(X6712,bool),fun(X6712,bool)),semilattice_sup_sup(fun(X6712,bool)),X6713),X6714) = ti(fun(X6712,bool),X6714) )
      & ( hAPP(fun(X6712,bool),fun(X6712,bool),hAPP(fun(X6712,bool),fun(fun(X6712,bool),fun(X6712,bool)),semilattice_sup_sup(fun(X6712,bool)),X6713),X6714) != ti(fun(X6712,bool),X6714)
        | hBOOL(hAPP(fun(X6712,bool),bool,hAPP(fun(X6712,bool),fun(fun(X6712,bool),bool),ord_less_eq(fun(X6712,bool)),X6713),X6714)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_784_subset__Un__eq])]) ).

fof(i_0_1333,plain,
    ! [X6718,X6719,X6720] :
      ( ~ hBOOL(hAPP(fun(X6718,bool),bool,hAPP(fun(X6718,bool),fun(fun(X6718,bool),bool),ord_less_eq(fun(X6718,bool)),X6719),X6720))
      | hAPP(fun(X6718,bool),fun(X6718,bool),hAPP(fun(X6718,bool),fun(fun(X6718,bool),fun(X6718,bool)),semilattice_sup_sup(fun(X6718,bool)),X6720),X6719) = ti(fun(X6718,bool),X6720) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_786_Un__absorb2])]) ).

fof(i_0_1334,plain,
    ! [X7206,X7207,X7208] :
      ( ~ hBOOL(hAPP(fun(X7206,bool),bool,hAPP(fun(X7206,bool),fun(fun(X7206,bool),bool),ord_less_eq(fun(X7206,bool)),X7207),X7208))
      | hAPP(fun(X7206,bool),fun(X7206,bool),hAPP(fun(X7206,bool),fun(fun(X7206,bool),fun(X7206,bool)),semilattice_inf_inf(fun(X7206,bool)),X7207),X7208) = ti(fun(X7206,bool),X7207) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_912_Int__absorb2])]) ).

fof(i_0_1335,plain,
    ! [X7203,X7204,X7205] :
      ( ~ hBOOL(hAPP(fun(X7203,bool),bool,hAPP(fun(X7203,bool),fun(fun(X7203,bool),bool),ord_less_eq(fun(X7203,bool)),X7204),X7205))
      | hAPP(fun(X7203,bool),fun(X7203,bool),hAPP(fun(X7203,bool),fun(fun(X7203,bool),fun(X7203,bool)),semilattice_inf_inf(fun(X7203,bool)),X7205),X7204) = ti(fun(X7203,bool),X7204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_911_Int__absorb1])]) ).

fof(i_0_1336,plain,
    ! [X4280,X4281,X4282] :
      ( ( ~ hBOOL(hAPP(X4280,bool,hAPP(X4280,fun(X4280,bool),ord_less_eq(X4280),X4281),X4282))
        | ti(X4280,X4281) = ti(X4280,X4282)
        | hBOOL(hAPP(X4280,bool,hAPP(X4280,fun(X4280,bool),ord_less(X4280),X4281),X4282))
        | ~ linorder(X4280) )
      & ( ti(X4280,X4281) != ti(X4280,X4282)
        | hBOOL(hAPP(X4280,bool,hAPP(X4280,fun(X4280,bool),ord_less_eq(X4280),X4281),X4282))
        | hBOOL(hAPP(X4280,bool,hAPP(X4280,fun(X4280,bool),ord_less(X4280),X4281),X4282))
        | ~ linorder(X4280) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1172])])])]) ).

fof(i_0_1337,plain,
    ! [X4304,X4305,X4306] :
      ( ~ order(X4304)
      | ~ hBOOL(hAPP(X4304,bool,hAPP(X4304,fun(X4304,bool),ord_less_eq(X4304),X4305),X4306))
      | ti(X4304,X4306) = ti(X4304,X4305)
      | hBOOL(hAPP(X4304,bool,hAPP(X4304,fun(X4304,bool),ord_less(X4304),X4305),X4306)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_127_xt1_I11_J])])]) ).

fof(i_0_1338,plain,
    ! [X4301,X4302,X4303] :
      ( ~ order(X4301)
      | ~ hBOOL(hAPP(X4301,bool,hAPP(X4301,fun(X4301,bool),ord_less_eq(X4301),X4302),X4303))
      | ti(X4301,X4302) = ti(X4301,X4303)
      | hBOOL(hAPP(X4301,bool,hAPP(X4301,fun(X4301,bool),ord_less(X4301),X4302),X4303)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_126_order__le__neq__trans])])]) ).

fof(i_0_1339,plain,
    ! [X4298,X4299,X4300] :
      ( ~ order(X4298)
      | ~ hBOOL(hAPP(X4298,bool,hAPP(X4298,fun(X4298,bool),ord_less_eq(X4298),X4299),X4300))
      | hBOOL(hAPP(X4298,bool,hAPP(X4298,fun(X4298,bool),ord_less(X4298),X4299),X4300))
      | ti(X4298,X4299) = ti(X4298,X4300) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_order__le__imp__less__or__eq])])]) ).

fof(i_0_1340,plain,
    ! [X4283,X4284,X4285] :
      ( ~ order(X4283)
      | ti(X4283,X4284) = ti(X4283,X4285)
      | ~ hBOOL(hAPP(X4283,bool,hAPP(X4283,fun(X4283,bool),ord_less_eq(X4283),X4284),X4285))
      | hBOOL(hAPP(X4283,bool,hAPP(X4283,fun(X4283,bool),ord_less(X4283),X4284),X4285)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_120_order__neq__le__trans])])]) ).

fof(i_0_1341,plain,
    ! [X4271,X4272,X4273] :
      ( ( ~ hBOOL(hAPP(X4271,bool,hAPP(X4271,fun(X4271,bool),ord_less_eq(X4271),X4272),X4273))
        | hBOOL(hAPP(X4271,bool,hAPP(X4271,fun(X4271,bool),ord_less(X4271),X4272),X4273))
        | ti(X4271,X4272) = ti(X4271,X4273)
        | ~ order(X4271) )
      & ( ~ hBOOL(hAPP(X4271,bool,hAPP(X4271,fun(X4271,bool),ord_less(X4271),X4272),X4273))
        | hBOOL(hAPP(X4271,bool,hAPP(X4271,fun(X4271,bool),ord_less_eq(X4271),X4272),X4273))
        | ~ order(X4271) )
      & ( ti(X4271,X4272) != ti(X4271,X4273)
        | hBOOL(hAPP(X4271,bool,hAPP(X4271,fun(X4271,bool),ord_less_eq(X4271),X4272),X4273))
        | ~ order(X4271) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_order__le__less])])])]) ).

fof(i_0_1342,plain,
    ! [X4265,X4266,X4267] :
      ( ( hBOOL(hAPP(X4265,bool,hAPP(X4265,fun(X4265,bool),ord_less_eq(X4265),X4266),X4267))
        | ~ hBOOL(hAPP(X4265,bool,hAPP(X4265,fun(X4265,bool),ord_less(X4265),X4266),X4267))
        | ~ order(X4265) )
      & ( ti(X4265,X4266) != ti(X4265,X4267)
        | ~ hBOOL(hAPP(X4265,bool,hAPP(X4265,fun(X4265,bool),ord_less(X4265),X4266),X4267))
        | ~ order(X4265) )
      & ( ~ hBOOL(hAPP(X4265,bool,hAPP(X4265,fun(X4265,bool),ord_less_eq(X4265),X4266),X4267))
        | ti(X4265,X4266) = ti(X4265,X4267)
        | hBOOL(hAPP(X4265,bool,hAPP(X4265,fun(X4265,bool),ord_less(X4265),X4266),X4267))
        | ~ order(X4265) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_order__less__le])])])]) ).

fof(i_0_1343,plain,
    ! [X4286,X4287,X4288] :
      ( ~ order(X4286)
      | ti(X4286,X4287) = ti(X4286,X4288)
      | ~ hBOOL(hAPP(X4286,bool,hAPP(X4286,fun(X4286,bool),ord_less_eq(X4286),X4288),X4287))
      | hBOOL(hAPP(X4286,bool,hAPP(X4286,fun(X4286,bool),ord_less(X4286),X4288),X4287)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_121_xt1_I12_J])])]) ).

fof(i_0_1344,plain,
    ! [X4378,X4379,X4380,X4381,X4382] :
      ( ( hAPP(X4378,X4379,X4382,X4380) != hAPP(X4378,X4379,X4382,X4381)
        | ti(X4378,X4380) = ti(X4378,X4381)
        | ~ hBOOL(hAPP(fun(X4378,bool),bool,hAPP(fun(X4378,X4379),fun(fun(X4378,bool),bool),inj_on(X4378,X4379),X4382),top_top(fun(X4378,bool)))) )
      & ( ti(X4378,X4380) != ti(X4378,X4381)
        | hAPP(X4378,X4379,X4382,X4380) = hAPP(X4378,X4379,X4382,X4381)
        | ~ hBOOL(hAPP(fun(X4378,bool),bool,hAPP(fun(X4378,X4379),fun(fun(X4378,bool),bool),inj_on(X4378,X4379),X4382),top_top(fun(X4378,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_inj__eq])])]) ).

fof(i_0_1345,plain,
    ! [X4383,X4384,X4385,X4386,X4387] :
      ( ~ hBOOL(hAPP(fun(X4383,bool),bool,hAPP(fun(X4383,X4384),fun(fun(X4383,bool),bool),inj_on(X4383,X4384),X4387),top_top(fun(X4383,bool))))
      | hAPP(X4383,X4384,X4387,X4385) != hAPP(X4383,X4384,X4387,X4386)
      | ti(X4383,X4385) = ti(X4383,X4386) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_injD])]) ).

fof(i_0_1346,plain,
    ! [X30,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X30))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X30))
            & ! [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_369_ex__least__nat__le]) ).

fof(i_0_1347,plain,
    ! [X1,X40] :
      ( ~ 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),X40))
       => ? [X19] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X19),X40)) ) ),
    inference(fof_simplification,[status(thm)],[fact_302_ex__new__if__finite]) ).

fof(i_0_1348,plain,
    ! [X5713,X5714] :
      ( ( hAPP(X5713,X5713,hAPP(X5713,fun(X5713,X5713),plus_plus(X5713),X5714),X5714) != zero_zero(X5713)
        | ti(X5713,X5714) = zero_zero(X5713)
        | ~ hBOOL(hAPP(fun(X5713,bool),bool,hAPP(X5713,fun(fun(X5713,bool),bool),member(X5713),X5714),ring_1_Ints(X5713)))
        | ~ ring_char_0(X5713) )
      & ( ti(X5713,X5714) != zero_zero(X5713)
        | hAPP(X5713,X5713,hAPP(X5713,fun(X5713,X5713),plus_plus(X5713),X5714),X5714) = zero_zero(X5713)
        | ~ hBOOL(hAPP(fun(X5713,bool),bool,hAPP(X5713,fun(fun(X5713,bool),bool),member(X5713),X5714),ring_1_Ints(X5713)))
        | ~ ring_char_0(X5713) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_541_Ints__double__eq__0__iff])])])]) ).

fof(i_0_1349,plain,
    ! [X5007,X5008,X5009,X5010] :
      ( ( hBOOL(hAPP(fun(X5008,bool),bool,hAPP(X5008,fun(fun(X5008,bool),bool),member(X5008),esk77_4(X5007,X5008,X5009,X5010)),X5010))
        | hBOOL(hAPP(fun(X5008,bool),bool,hAPP(fun(X5008,X5007),fun(fun(X5008,bool),bool),inj_on(X5008,X5007),X5009),X5010)) )
      & ( hBOOL(hAPP(fun(X5008,bool),bool,hAPP(X5008,fun(fun(X5008,bool),bool),member(X5008),esk78_4(X5007,X5008,X5009,X5010)),X5010))
        | hBOOL(hAPP(fun(X5008,bool),bool,hAPP(fun(X5008,X5007),fun(fun(X5008,bool),bool),inj_on(X5008,X5007),X5009),X5010)) )
      & ( hAPP(X5008,X5007,X5009,esk77_4(X5007,X5008,X5009,X5010)) = hAPP(X5008,X5007,X5009,esk78_4(X5007,X5008,X5009,X5010))
        | hBOOL(hAPP(fun(X5008,bool),bool,hAPP(fun(X5008,X5007),fun(fun(X5008,bool),bool),inj_on(X5008,X5007),X5009),X5010)) )
      & ( ti(X5008,esk77_4(X5007,X5008,X5009,X5010)) != ti(X5008,esk78_4(X5007,X5008,X5009,X5010))
        | hBOOL(hAPP(fun(X5008,bool),bool,hAPP(fun(X5008,X5007),fun(fun(X5008,bool),bool),inj_on(X5008,X5007),X5009),X5010)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_317_inj__onI])])])])]) ).

fof(i_0_1350,plain,
    ! [X3836,X3837] : ti(fun(fun(X3836,fun(X3836,X3836)),fun(fun(X3837,X3836),fun(X3836,fun(fun(X3837,bool),X3836)))),finite_fold_image(X3836,X3837)) = finite_fold_image(X3836,X3837),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofold__image_res]) ).

fof(i_0_1351,plain,
    ! [X4472,X4473,X4474] :
      ( ~ linordered_idom(X4472)
      | ti(X4472,X4473) = ti(X4472,X4474)
      | hBOOL(hAPP(X4472,bool,hAPP(X4472,fun(X4472,bool),ord_less(X4472),X4473),X4474))
      | hBOOL(hAPP(X4472,bool,hAPP(X4472,fun(X4472,bool),ord_less(X4472),X4474),X4473)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1173])])]) ).

fof(i_0_1352,plain,
    ! [X4116,X4117,X4118] :
      ( ( ti(X4116,X4117) = ti(X4116,X4118)
        | hBOOL(hAPP(X4116,bool,hAPP(X4116,fun(X4116,bool),ord_less(X4116),X4117),X4118))
        | hBOOL(hAPP(X4116,bool,hAPP(X4116,fun(X4116,bool),ord_less(X4116),X4118),X4117))
        | ~ linorder(X4116) )
      & ( ~ hBOOL(hAPP(X4116,bool,hAPP(X4116,fun(X4116,bool),ord_less(X4116),X4117),X4118))
        | ti(X4116,X4117) != ti(X4116,X4118)
        | ~ linorder(X4116) )
      & ( ~ hBOOL(hAPP(X4116,bool,hAPP(X4116,fun(X4116,bool),ord_less(X4116),X4118),X4117))
        | ti(X4116,X4117) != ti(X4116,X4118)
        | ~ linorder(X4116) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_linorder__neq__iff])])])]) ).

fof(i_0_1353,plain,
    ! [X4113,X4114,X4115] :
      ( ( hBOOL(hAPP(X4113,bool,hAPP(X4113,fun(X4113,bool),ord_less(X4113),X4114),X4115))
        | hBOOL(hAPP(X4113,bool,hAPP(X4113,fun(X4113,bool),ord_less(X4113),X4115),X4114))
        | ti(X4113,X4114) = ti(X4113,X4115)
        | ~ linorder(X4113) )
      & ( ~ hBOOL(hAPP(X4113,bool,hAPP(X4113,fun(X4113,bool),ord_less(X4113),X4115),X4114))
        | ~ hBOOL(hAPP(X4113,bool,hAPP(X4113,fun(X4113,bool),ord_less(X4113),X4114),X4115))
        | ~ linorder(X4113) )
      & ( ti(X4113,X4114) != ti(X4113,X4115)
        | ~ hBOOL(hAPP(X4113,bool,hAPP(X4113,fun(X4113,bool),ord_less(X4113),X4114),X4115))
        | ~ linorder(X4113) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1174])])])]) ).

fof(i_0_1354,plain,
    ! [X4110,X4111,X4112] :
      ( ~ linorder(X4110)
      | hBOOL(hAPP(X4110,bool,hAPP(X4110,fun(X4110,bool),ord_less(X4110),X4111),X4112))
      | ti(X4110,X4111) = ti(X4110,X4112)
      | hBOOL(hAPP(X4110,bool,hAPP(X4110,fun(X4110,bool),ord_less(X4110),X4112),X4111)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_linorder__less__linear])])]) ).

fof(i_0_1355,plain,
    ! [X4104,X4105,X4106] :
      ( ~ linorder(X4104)
      | ti(X4104,X4105) = ti(X4104,X4106)
      | hBOOL(hAPP(X4104,bool,hAPP(X4104,fun(X4104,bool),ord_less(X4104),X4105),X4106))
      | hBOOL(hAPP(X4104,bool,hAPP(X4104,fun(X4104,bool),ord_less(X4104),X4106),X4105)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1175])])]) ).

fof(i_0_1356,plain,
    ! [X4049,X4050,X4051] :
      ( ~ linorder(X4049)
      | hBOOL(hAPP(X4049,bool,hAPP(X4049,fun(X4049,bool),ord_less(X4049),X4050),X4051))
      | ti(X4049,X4050) = ti(X4049,X4051)
      | hBOOL(hAPP(X4049,bool,hAPP(X4049,fun(X4049,bool),ord_less(X4049),X4051),X4050)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1176])])]) ).

fof(i_0_1357,plain,
    ! [X6464,X6465,X6466,X6467,X6468,X6469,X6470] :
      ( hAPP(fun(X6464,X6465),fun(X6464,X6466),hAPP(fun(X6465,X6466),fun(fun(X6464,X6465),fun(X6464,X6466)),comp(X6465,X6466,X6464),X6468),X6469) != ti(fun(X6464,X6466),X6470)
      | hAPP(X6465,X6466,X6468,hAPP(X6464,X6465,X6469,X6467)) = hAPP(X6464,X6466,X6470,X6467) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_734_o__eq__dest__lhs])]) ).

fof(i_0_1358,plain,
    ! [X6946,X6947,X6948] :
      ( ~ semilattice_sup(X6946)
      | ~ hBOOL(hAPP(X6946,bool,hAPP(X6946,fun(X6946,bool),ord_less_eq(X6946),X6947),X6948))
      | hAPP(X6946,X6946,hAPP(X6946,fun(X6946,X6946),semilattice_sup_sup(X6946),X6947),X6948) = ti(X6946,X6948) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_844_sup__absorb2])])]) ).

fof(i_0_1359,plain,
    ! [X6931,X6932,X6933] :
      ( ( ~ hBOOL(hAPP(X6931,bool,hAPP(X6931,fun(X6931,bool),ord_less_eq(X6931),X6932),X6933))
        | hAPP(X6931,X6931,hAPP(X6931,fun(X6931,X6931),semilattice_sup_sup(X6931),X6932),X6933) = ti(X6931,X6933)
        | ~ semilattice_sup(X6931) )
      & ( hAPP(X6931,X6931,hAPP(X6931,fun(X6931,X6931),semilattice_sup_sup(X6931),X6932),X6933) != ti(X6931,X6933)
        | hBOOL(hAPP(X6931,bool,hAPP(X6931,fun(X6931,bool),ord_less_eq(X6931),X6932),X6933))
        | ~ semilattice_sup(X6931) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_840_le__iff__sup])])])]) ).

fof(i_0_1360,plain,
    ! [X6949,X6950,X6951] :
      ( ~ semilattice_sup(X6949)
      | ~ hBOOL(hAPP(X6949,bool,hAPP(X6949,fun(X6949,bool),ord_less_eq(X6949),X6950),X6951))
      | hAPP(X6949,X6949,hAPP(X6949,fun(X6949,X6949),semilattice_sup_sup(X6949),X6951),X6950) = ti(X6949,X6951) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_845_sup__absorb1])])]) ).

fof(i_0_1361,plain,
    ! [X7274,X7275,X7276] :
      ( ( ~ hBOOL(hAPP(X7274,bool,hAPP(X7274,fun(X7274,bool),ord_less_eq(X7274),X7275),X7276))
        | hAPP(X7274,X7274,hAPP(X7274,fun(X7274,X7274),semilattice_inf_inf(X7274),X7275),X7276) = ti(X7274,X7275)
        | ~ semilattice_inf(X7274) )
      & ( hAPP(X7274,X7274,hAPP(X7274,fun(X7274,X7274),semilattice_inf_inf(X7274),X7275),X7276) != ti(X7274,X7275)
        | hBOOL(hAPP(X7274,bool,hAPP(X7274,fun(X7274,bool),ord_less_eq(X7274),X7275),X7276))
        | ~ semilattice_inf(X7274) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_929_le__iff__inf])])])]) ).

fof(i_0_1362,plain,
    ! [X7259,X7260,X7261] :
      ( ~ semilattice_inf(X7259)
      | ~ hBOOL(hAPP(X7259,bool,hAPP(X7259,fun(X7259,bool),ord_less_eq(X7259),X7260),X7261))
      | hAPP(X7259,X7259,hAPP(X7259,fun(X7259,X7259),semilattice_inf_inf(X7259),X7260),X7261) = ti(X7259,X7260) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_925_inf__absorb1])])]) ).

fof(i_0_1363,plain,
    ! [X7256,X7257,X7258] :
      ( ~ semilattice_inf(X7256)
      | ~ hBOOL(hAPP(X7256,bool,hAPP(X7256,fun(X7256,bool),ord_less_eq(X7256),X7257),X7258))
      | hAPP(X7256,X7256,hAPP(X7256,fun(X7256,X7256),semilattice_inf_inf(X7256),X7258),X7257) = ti(X7256,X7257) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_924_inf__absorb2])])]) ).

fof(i_0_1364,plain,
    ! [X3976,X3977,X3978,X3979,X3980,X3981] :
      ( ( ti(X3977,X3978) = ti(X3977,X3980)
        | hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3978),X3979) != hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3980),X3981) )
      & ( ti(X3976,X3979) = ti(X3976,X3981)
        | hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3978),X3979) != hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3980),X3981) )
      & ( ti(X3977,X3978) != ti(X3977,X3980)
        | ti(X3976,X3979) != ti(X3976,X3981)
        | hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3978),X3979) = hAPP(X3976,product_prod(X3977,X3976),hAPP(X3977,fun(X3976,product_prod(X3977,X3976)),product_Pair(X3977,X3976),X3980),X3981) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_Pair__eq])])]) ).

fof(i_0_1365,plain,
    ! [X3970,X3971,X3972,X3973,X3974,X3975] :
      ( ( ti(X3971,X3972) = ti(X3971,X3974)
        | hAPP(X3970,product_prod(X3971,X3970),hAPP(X3971,fun(X3970,product_prod(X3971,X3970)),product_Pair(X3971,X3970),X3972),X3973) != hAPP(X3970,product_prod(X3971,X3970),hAPP(X3971,fun(X3970,product_prod(X3971,X3970)),product_Pair(X3971,X3970),X3974),X3975) )
      & ( ti(X3970,X3973) = ti(X3970,X3975)
        | hAPP(X3970,product_prod(X3971,X3970),hAPP(X3971,fun(X3970,product_prod(X3971,X3970)),product_Pair(X3971,X3970),X3972),X3973) != hAPP(X3970,product_prod(X3971,X3970),hAPP(X3971,fun(X3970,product_prod(X3971,X3970)),product_Pair(X3971,X3970),X3974),X3975) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_Pair__inject])])]) ).

fof(i_0_1366,plain,
    ! [X6362,X6363] :
      ( ~ hBOOL(hAPP(fun(X6362,bool),bool,hAPP(X6362,fun(fun(X6362,bool),bool),member(X6362),esk149_2(X6362,X6363)),X6363))
      | top_top(fun(X6362,bool)) = ti(fun(X6362,bool),X6363) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_715_UNIV__eq__I])])]) ).

fof(i_0_1367,plain,
    ! [X3855,X3856,X3857] : ti(fun(fun(X3855,bool),fun(fun(X3856,X3857),fun(fun(X3855,X3856),fun(X3855,X3857)))),compose(X3855,X3856,X3857)) = compose(X3855,X3856,X3857),
    inference(variable_rename,[status(thm)],[tsy_c_FuncSet_Ocompose_res]) ).

fof(i_0_1368,plain,
    ! [X4101,X4102,X4103] :
      ( ~ order(X4101)
      | ~ hBOOL(hAPP(X4101,bool,hAPP(X4101,fun(X4101,bool),ord_less(X4101),X4102),X4103))
      | ti(X4101,X4102) != ti(X4101,X4103) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_less__imp__neq])])]) ).

fof(i_0_1369,plain,
    ! [X4092,X4093,X4094] :
      ( ~ order(X4092)
      | ~ hBOOL(hAPP(X4092,bool,hAPP(X4092,fun(X4092,bool),ord_less(X4092),X4093),X4094))
      | ti(X4092,X4093) != ti(X4092,X4094) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_order__less__imp__not__eq])])]) ).

fof(i_0_1370,plain,
    ! [X4089,X4090,X4091] :
      ( ~ order(X4089)
      | ~ hBOOL(hAPP(X4089,bool,hAPP(X4089,fun(X4089,bool),ord_less(X4089),X4090),X4091))
      | ti(X4089,X4091) != ti(X4089,X4090) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_order__less__imp__not__eq2])])]) ).

fof(i_0_1371,plain,
    ! [X4422,X4423,X4424] :
      ( ( hAPP(X4422,X4423,X4424,esk35_3(X4422,X4423,X4424)) = hAPP(X4422,X4423,X4424,esk36_3(X4422,X4423,X4424))
        | hBOOL(hAPP(fun(X4422,bool),bool,hAPP(fun(X4422,X4423),fun(fun(X4422,bool),bool),inj_on(X4422,X4423),X4424),top_top(fun(X4422,bool)))) )
      & ( ti(X4422,esk35_3(X4422,X4423,X4424)) != ti(X4422,esk36_3(X4422,X4423,X4424))
        | hBOOL(hAPP(fun(X4422,bool),bool,hAPP(fun(X4422,X4423),fun(fun(X4422,bool),bool),inj_on(X4422,X4423),X4424),top_top(fun(X4422,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_154_injI])])])]) ).

fof(i_0_1372,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X35))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_95_linorder__le__cases]) ).

fof(i_0_1373,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X34,X35] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_117_leI]) ).

fof(i_0_1374,plain,
    ! [X1] :
      ( linorder(X1)
     => ! [X35,X34] :
          ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X35),X34))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X35)) ) ),
    inference(fof_simplification,[status(thm)],[fact_118_not__leE]) ).

fof(i_0_1375,plain,
    ! [X4677,X4678,X4679] :
      ( ti(fun(X4677,bool),X4678) != ti(fun(X4677,bool),X4679)
      | hBOOL(hAPP(fun(X4677,bool),bool,hAPP(fun(X4677,bool),fun(fun(X4677,bool),bool),ord_less_eq(fun(X4677,bool)),X4678),X4679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_210_equalityD1])]) ).

fof(i_0_1376,plain,
    ! [X4645,X4646,X4647] :
      ( ( hBOOL(hAPP(fun(X4645,bool),bool,hAPP(fun(X4645,bool),fun(fun(X4645,bool),bool),ord_less_eq(fun(X4645,bool)),X4646),X4647))
        | ti(fun(X4645,bool),X4646) != ti(fun(X4645,bool),X4647) )
      & ( hBOOL(hAPP(fun(X4645,bool),bool,hAPP(fun(X4645,bool),fun(fun(X4645,bool),bool),ord_less_eq(fun(X4645,bool)),X4647),X4646))
        | ti(fun(X4645,bool),X4646) != ti(fun(X4645,bool),X4647) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1177])])]) ).

fof(i_0_1377,plain,
    ! [X4674,X4675,X4676] :
      ( ti(fun(X4674,bool),X4675) != ti(fun(X4674,bool),X4676)
      | hBOOL(hAPP(fun(X4674,bool),bool,hAPP(fun(X4674,bool),fun(fun(X4674,bool),bool),ord_less_eq(fun(X4674,bool)),X4676),X4675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_209_equalityD2])]) ).

fof(i_0_1378,plain,
    ! [X3838,X3839] : ti(fun(fun(X3838,fun(X3839,X3839)),fun(fun(fun(X3838,bool),fun(X3839,X3839)),bool)),finite_folding_idem(X3838,X3839)) = finite_folding_idem(X3838,X3839),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofolding__idem_res]) ).

fof(i_0_1379,plain,
    ! [X3901] : ti(fun(fun(X3901,nat),fun(fun(product_prod(X3901,X3901),bool),fun(product_prod(X3901,X3901),bool))),mlex_prod(X3901)) = mlex_prod(X3901),
    inference(variable_rename,[status(thm)],[tsy_c_Wellfounded_Omlex__prod_res]) ).

fof(i_0_1380,plain,
    ! [X3853,X3854] : ti(fun(fun(X3853,bool),fun(fun(X3853,fun(X3854,bool)),fun(fun(X3853,X3854),bool))),pi(X3853,X3854)) = pi(X3853,X3854),
    inference(variable_rename,[status(thm)],[tsy_c_FuncSet_OPi_res]) ).

fof(i_0_1381,plain,
    ! [X34,X35] :
      ( X34 != X35
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X35))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_217_linorder__neqE__nat]) ).

fof(i_0_1382,plain,
    ! [X4487,X4488,X4489,X4490] :
      ( ( hAPP(X4487,X4487,hAPP(X4487,fun(X4487,X4487),plus_plus(X4487),X4488),X4489) != hAPP(X4487,X4487,hAPP(X4487,fun(X4487,X4487),plus_plus(X4487),X4490),X4489)
        | ti(X4487,X4488) = ti(X4487,X4490)
        | ~ cancel_semigroup_add(X4487) )
      & ( ti(X4487,X4488) != ti(X4487,X4490)
        | hAPP(X4487,X4487,hAPP(X4487,fun(X4487,X4487),plus_plus(X4487),X4488),X4489) = hAPP(X4487,X4487,hAPP(X4487,fun(X4487,X4487),plus_plus(X4487),X4490),X4489)
        | ~ cancel_semigroup_add(X4487) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_add__right__cancel])])])]) ).

fof(i_0_1383,plain,
    ! [X4475,X4476,X4477,X4478] :
      ( ~ cancel_semigroup_add(X4475)
      | hAPP(X4475,X4475,hAPP(X4475,fun(X4475,X4475),plus_plus(X4475),X4476),X4477) != hAPP(X4475,X4475,hAPP(X4475,fun(X4475,X4475),plus_plus(X4475),X4478),X4477)
      | ti(X4475,X4476) = ti(X4475,X4478) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_165_add__right__imp__eq])])]) ).

fof(i_0_1384,plain,
    ! [X4479,X4480,X4481,X4482] :
      ( ~ cancel146912293up_add(X4479)
      | hAPP(X4479,X4479,hAPP(X4479,fun(X4479,X4479),plus_plus(X4479),X4480),X4481) != hAPP(X4479,X4479,hAPP(X4479,fun(X4479,X4479),plus_plus(X4479),X4480),X4482)
      | ti(X4479,X4481) = ti(X4479,X4482) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_add__imp__eq])])]) ).

fof(i_0_1385,plain,
    ! [X4491,X4492,X4493,X4494] :
      ( ( hAPP(X4491,X4491,hAPP(X4491,fun(X4491,X4491),plus_plus(X4491),X4492),X4493) != hAPP(X4491,X4491,hAPP(X4491,fun(X4491,X4491),plus_plus(X4491),X4492),X4494)
        | ti(X4491,X4493) = ti(X4491,X4494)
        | ~ cancel_semigroup_add(X4491) )
      & ( ti(X4491,X4493) != ti(X4491,X4494)
        | hAPP(X4491,X4491,hAPP(X4491,fun(X4491,X4491),plus_plus(X4491),X4492),X4493) = hAPP(X4491,X4491,hAPP(X4491,fun(X4491,X4491),plus_plus(X4491),X4492),X4494)
        | ~ cancel_semigroup_add(X4491) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_add__left__cancel])])])]) ).

fof(i_0_1386,plain,
    ! [X4483,X4484,X4485,X4486] :
      ( ~ cancel_semigroup_add(X4483)
      | hAPP(X4483,X4483,hAPP(X4483,fun(X4483,X4483),plus_plus(X4483),X4484),X4485) != hAPP(X4483,X4483,hAPP(X4483,fun(X4483,X4483),plus_plus(X4483),X4484),X4486)
      | ti(X4483,X4485) = ti(X4483,X4486) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_167_add__left__imp__eq])])]) ).

fof(i_0_1387,plain,
    ! [X4121,X4122,X4123,X4124] :
      ( hAPP(X4121,X4122,X4123,esk21_4(X4121,X4122,X4123,X4124)) != hAPP(X4121,X4122,X4124,esk21_4(X4121,X4122,X4123,X4124))
      | ti(fun(X4121,X4122),X4123) = ti(fun(X4121,X4122),X4124) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_ext])])]) ).

fof(i_0_1388,plain,
    ! [X7631,X7632,X7633] :
      ( ~ hBOOL(hAPP(X7631,bool,hAPP(X7631,fun(X7631,bool),fequal(X7631),X7632),X7633))
      | ti(X7631,X7632) = ti(X7631,X7633) ),
    inference(variable_rename,[status(thm)],[i_0_1178]) ).

fof(i_0_1389,plain,
    ! [X4022,X4023] :
      ( ( ti(X4022,X4023) = top_top(X4022)
        | hBOOL(hAPP(X4022,bool,hAPP(X4022,fun(X4022,bool),ord_less(X4022),X4023),top_top(X4022)))
        | ~ top(X4022) )
      & ( ~ hBOOL(hAPP(X4022,bool,hAPP(X4022,fun(X4022,bool),ord_less(X4022),X4023),top_top(X4022)))
        | ti(X4022,X4023) != top_top(X4022)
        | ~ top(X4022) ) ),
    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_1390,plain,
    ! [X5675,X5676,X5677,X5678,X5680,X5681,X5682,X5684] :
      ( ( hAPP(fun(X5675,bool),fun(X5676,bool),hAPP(fun(X5675,X5676),fun(fun(X5675,bool),fun(X5676,bool)),image(X5675,X5676),X5677),top_top(fun(X5675,bool))) != top_top(fun(X5676,bool))
        | ti(X5676,X5678) = hAPP(X5675,X5676,X5677,esk129_4(X5675,X5676,X5677,X5678)) )
      & ( ti(X5681,esk130_3(X5680,X5681,X5682)) != hAPP(X5680,X5681,X5682,X5684)
        | hAPP(fun(X5680,bool),fun(X5681,bool),hAPP(fun(X5680,X5681),fun(fun(X5680,bool),fun(X5681,bool)),image(X5680,X5681),X5682),top_top(fun(X5680,bool))) = top_top(fun(X5681,bool)) ) ),
    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_529_surj__def])])])])]) ).

fof(i_0_1391,plain,
    ! [X5665,X5666,X5667,X5668] :
      ( hAPP(fun(X5665,bool),fun(X5666,bool),hAPP(fun(X5665,X5666),fun(fun(X5665,bool),fun(X5666,bool)),image(X5665,X5666),X5668),top_top(fun(X5665,bool))) != top_top(fun(X5666,bool))
      | ti(X5666,X5667) = hAPP(X5665,X5666,X5668,esk127_4(X5665,X5666,X5667,X5668)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_527_surjD])])]) ).

fof(i_0_1392,plain,
    ! [X5660,X5661,X5662,X5663] :
      ( hAPP(fun(X5660,bool),fun(X5661,bool),hAPP(fun(X5660,X5661),fun(fun(X5660,bool),fun(X5661,bool)),image(X5660,X5661),X5663),top_top(fun(X5660,bool))) != top_top(fun(X5661,bool))
      | ti(X5661,X5662) = hAPP(X5660,X5661,X5663,esk126_4(X5660,X5661,X5662,X5663)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_526_surjE])])]) ).

fof(i_0_1393,plain,
    ! [X4327,X4328] :
      ( ~ top(X4327)
      | ~ hBOOL(hAPP(X4327,bool,hAPP(X4327,fun(X4327,bool),ord_less_eq(X4327),top_top(X4327)),X4328))
      | ti(X4327,X4328) = top_top(X4327) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_top__le])])]) ).

fof(i_0_1394,plain,
    ! [X4325,X4326] :
      ( ( ~ hBOOL(hAPP(X4325,bool,hAPP(X4325,fun(X4325,bool),ord_less_eq(X4325),top_top(X4325)),X4326))
        | ti(X4325,X4326) = top_top(X4325)
        | ~ top(X4325) )
      & ( ti(X4325,X4326) != top_top(X4325)
        | hBOOL(hAPP(X4325,bool,hAPP(X4325,fun(X4325,bool),ord_less_eq(X4325),top_top(X4325)),X4326))
        | ~ top(X4325) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_top__unique])])])]) ).

fof(i_0_1395,plain,
    ! [X7081,X7082,X7083] :
      ( ~ lattice(X7081)
      | hAPP(X7081,X7081,hAPP(X7081,fun(X7081,X7081),semilattice_sup_sup(X7081),X7082),hAPP(X7081,X7081,hAPP(X7081,fun(X7081,X7081),semilattice_inf_inf(X7081),X7082),X7083)) = ti(X7081,X7082) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_880_sup__inf__absorb])])]) ).

fof(i_0_1396,plain,
    ! [X7084,X7085,X7086] :
      ( ~ lattice(X7084)
      | hAPP(X7084,X7084,hAPP(X7084,fun(X7084,X7084),semilattice_inf_inf(X7084),X7085),hAPP(X7084,X7084,hAPP(X7084,fun(X7084,X7084),semilattice_sup_sup(X7084),X7085),X7086)) = ti(X7084,X7085) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_881_inf__sup__absorb])])]) ).

fof(i_0_1397,plain,
    ! [X1] :
      ( linordered_semidom(X1)
     => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
    inference(fof_simplification,[status(thm)],[fact_353_not__one__le__zero]) ).

fof(i_0_1398,plain,
    ! [X1] :
      ( linordered_semidom(X1)
     => ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
    inference(fof_simplification,[status(thm)],[fact_355_not__one__less__zero]) ).

fof(i_0_1399,plain,
    ! [X5706,X5707,X5708] : hAPP(nat,X5706,hAPP(fun(nat,X5706),fun(nat,X5706),hAPP(X5706,fun(fun(nat,X5706),fun(nat,X5706)),nat_case(X5706),X5707),X5708),zero_zero(nat)) = ti(X5706,X5707),
    inference(variable_rename,[status(thm)],[fact_539_nat__case__0]) ).

fof(i_0_1400,plain,
    ! [X1] :
      ( top(X1)
     => ! [X21] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_30_not__top__less]) ).

fof(i_0_1401,plain,
    ! [X1] :
      ( preorder(X1)
     => ! [X34] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X34)) ),
    inference(fof_simplification,[status(thm)],[fact_74_order__less__irrefl]) ).

fof(i_0_1402,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_331_less__nat__zero__code]) ).

fof(i_0_1403,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_329_not__less0]) ).

fof(i_0_1404,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[fact_319_less__zeroE]) ).

fof(i_0_1405,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
    inference(fof_simplification,[status(thm)],[fact_218_less__irrefl__nat]) ).

fof(i_0_1406,plain,
    ! [X51] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X51)),
    inference(fof_simplification,[status(thm)],[fact_215_less__not__refl]) ).

fof(i_0_1407,plain,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119))
      | hBOOL(X118)
      | hBOOL(X119) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).

fof(i_0_1408,plain,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
      | hBOOL(X118) ),
    inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).

fof(i_0_1409,plain,
    ! [X118,X119] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119))
      | hBOOL(X119) ),
    inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).

fof(i_0_1410,plain,
    ! [X7634,X7635,X7636] :
      ( ti(X7634,X7635) != ti(X7634,X7636)
      | hBOOL(hAPP(X7634,bool,hAPP(X7634,fun(X7634,bool),fequal(X7634),X7635),X7636)) ),
    inference(variable_rename,[status(thm)],[help_fequal_2_1_T]) ).

fof(i_0_1411,plain,
    ! [X7584,X7585,X7586] : hAPP(X7584,X7584,hAPP(X7584,fun(X7584,X7584),hAPP(bool,fun(X7584,fun(X7584,X7584)),if(X7584),fTrue),X7585),X7586) = ti(X7584,X7585),
    inference(variable_rename,[status(thm)],[help_If_1_1_T]) ).

fof(i_0_1412,plain,
    ! [X7587,X7588,X7589] : hAPP(X7587,X7587,hAPP(X7587,fun(X7587,X7587),hAPP(bool,fun(X7587,fun(X7587,X7587)),if(X7587),fFalse),X7588),X7589) = ti(X7587,X7589),
    inference(variable_rename,[status(thm)],[help_If_2_1_T]) ).

fof(i_0_1413,plain,
    ! [X3897,X3898] : ti(fun(fun(X3897,bool),fun(fun(X3898,bool),fun(sum_sum(X3897,X3898),bool))),sum_Plus(X3897,X3898)) = sum_Plus(X3897,X3898),
    inference(variable_rename,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).

fof(i_0_1414,plain,
    ! [X4931,X4932] :
      ( ~ hBOOL(hAPP(fun(X4931,bool),bool,finite_finite_1(X4931),top_top(fun(X4931,bool))))
      | hAPP(fun(X4931,bool),nat,finite_card(X4931),X4932) != hAPP(fun(X4931,bool),nat,finite_card(X4931),top_top(fun(X4931,bool)))
      | ti(fun(X4931,bool),X4932) = top_top(fun(X4931,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_299_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_1415,plain,
    ! [X3831,X3832,X3833] : ti(fun(fun(X3831,fun(X3832,X3833)),fun(fun(X3831,X3832),fun(X3831,X3833))),combs(X3831,X3832,X3833)) = combs(X3831,X3832,X3833),
    inference(variable_rename,[status(thm)],[tsy_c_COMBS_res]) ).

fof(i_0_1416,plain,
    ! [X5313,X5314,X5315] :
      ( ( ti(X5313,X5314) != hAPP(X5313,X5313,hAPP(X5313,fun(X5313,X5313),plus_plus(X5313),X5314),X5315)
        | ti(X5313,X5315) = zero_zero(X5313)
        | ~ semiri456707255roduct(X5313) )
      & ( ti(X5313,X5315) != zero_zero(X5313)
        | ti(X5313,X5314) = hAPP(X5313,X5313,hAPP(X5313,fun(X5313,X5313),plus_plus(X5313),X5314),X5315)
        | ~ semiri456707255roduct(X5313) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_add__0__iff])])])]) ).

fof(i_0_1417,plain,
    ! [X5947,X5948,X5949] :
      ( ( hAPP(X5947,X5947,hAPP(X5947,fun(X5947,X5947),times_times(X5947),X5948),X5949) != zero_zero(X5947)
        | ti(X5947,X5948) = zero_zero(X5947)
        | ti(X5947,X5949) = zero_zero(X5947)
        | ~ ring_n68954251visors(X5947) )
      & ( ti(X5947,X5948) != zero_zero(X5947)
        | hAPP(X5947,X5947,hAPP(X5947,fun(X5947,X5947),times_times(X5947),X5948),X5949) = zero_zero(X5947)
        | ~ ring_n68954251visors(X5947) )
      & ( ti(X5947,X5949) != zero_zero(X5947)
        | hAPP(X5947,X5947,hAPP(X5947,fun(X5947,X5947),times_times(X5947),X5948),X5949) = zero_zero(X5947)
        | ~ ring_n68954251visors(X5947) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_596_mult__eq__0__iff])])])]) ).

fof(i_0_1418,plain,
    ! [X5944,X5945,X5946] :
      ( ~ no_zero_divisors(X5944)
      | ti(X5944,X5946) = zero_zero(X5944)
      | ti(X5944,X5945) = zero_zero(X5944)
      | hAPP(X5944,X5944,hAPP(X5944,fun(X5944,X5944),times_times(X5944),X5946),X5945) != zero_zero(X5944) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_595_no__zero__divisors])])]) ).

fof(i_0_1419,plain,
    ! [X5941,X5942,X5943] :
      ( ~ no_zero_divisors(X5941)
      | hAPP(X5941,X5941,hAPP(X5941,fun(X5941,X5941),times_times(X5941),X5942),X5943) != zero_zero(X5941)
      | ti(X5941,X5942) = zero_zero(X5941)
      | ti(X5941,X5943) = zero_zero(X5941) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_594_divisors__zero])])]) ).

fof(i_0_1420,plain,
    ! [X3885,X3886,X3887] : ti(fun(fun(X3885,fun(X3886,X3887)),fun(product_prod(X3885,X3886),X3887)),product_prod_rec(X3885,X3886,X3887)) = product_prod_rec(X3885,X3886,X3887),
    inference(variable_rename,[status(thm)],[tsy_c_Product__Type_Oprod_Oprod__rec_res]) ).

fof(i_0_1421,plain,
    ! [X3825,X3826,X3827] : ti(fun(fun(X3825,fun(X3826,X3827)),fun(X3826,fun(X3825,X3827))),combc(X3825,X3826,X3827)) = combc(X3825,X3826,X3827),
    inference(variable_rename,[status(thm)],[tsy_c_COMBC_res]) ).

fof(i_0_1422,plain,
    ! [X3846,X3847,X3848] : ti(fun(fun(X3846,X3847),fun(fun(X3848,X3846),fun(X3848,X3847))),comp(X3846,X3847,X3848)) = comp(X3846,X3847,X3848),
    inference(variable_rename,[status(thm)],[tsy_c_Fun_Ocomp_res]) ).

fof(i_0_1423,plain,
    ! [X3822,X3823,X3824] : ti(fun(fun(X3822,X3823),fun(fun(X3824,X3822),fun(X3824,X3823))),combb(X3822,X3823,X3824)) = combb(X3822,X3823,X3824),
    inference(variable_rename,[status(thm)],[tsy_c_COMBB_res]) ).

fof(i_0_1424,plain,
    ! [X7289,X7290,X7291] :
      ( ( ti(X7289,X7290) = top_top(X7289)
        | hAPP(X7289,X7289,hAPP(X7289,fun(X7289,X7289),semilattice_inf_inf(X7289),X7290),X7291) != top_top(X7289)
        | ~ bounded_lattice_top(X7289) )
      & ( ti(X7289,X7291) = top_top(X7289)
        | hAPP(X7289,X7289,hAPP(X7289,fun(X7289,X7289),semilattice_inf_inf(X7289),X7290),X7291) != top_top(X7289)
        | ~ bounded_lattice_top(X7289) )
      & ( ti(X7289,X7290) != top_top(X7289)
        | ti(X7289,X7291) != top_top(X7289)
        | hAPP(X7289,X7289,hAPP(X7289,fun(X7289,X7289),semilattice_inf_inf(X7289),X7290),X7291) = top_top(X7289)
        | ~ bounded_lattice_top(X7289) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_934_inf__eq__top__iff])])])]) ).

fof(i_0_1425,plain,
    ! [X7142,X7143] : hAPP(fun(X7142,bool),fun(X7142,bool),hAPP(fun(X7142,bool),fun(fun(X7142,bool),fun(X7142,bool)),semilattice_inf_inf(fun(X7142,bool)),top_top(fun(X7142,bool))),X7143) = ti(fun(X7142,bool),X7143),
    inference(variable_rename,[status(thm)],[fact_894_Int__UNIV__left]) ).

fof(i_0_1426,plain,
    ! [X3873,X3874] : ti(fun(fun(X3873,bool),fun(fun(X3873,X3874),fun(X3874,X3873))),hilbert_inv_into(X3873,X3874)) = hilbert_inv_into(X3873,X3874),
    inference(variable_rename,[status(thm)],[tsy_c_Hilbert__Choice_Oinv__into_res]) ).

fof(i_0_1427,plain,
    ! [X3851,X3852] : ti(fun(fun(X3851,bool),fun(fun(X3851,X3852),fun(X3852,X3851))),the_inv_into(X3851,X3852)) = the_inv_into(X3851,X3852),
    inference(variable_rename,[status(thm)],[tsy_c_Fun_Othe__inv__into_res]) ).

fof(i_0_1428,plain,
    ! [X3860,X3861] : ti(fun(fun(X3860,X3861),fun(fun(X3860,bool),fun(X3860,X3861))),restrict(X3860,X3861)) = restrict(X3860,X3861),
    inference(variable_rename,[status(thm)],[tsy_c_FuncSet_Orestrict_res]) ).

fof(i_0_1429,plain,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X39,X40] :
          ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X39),X40) = zero_zero(X2) ) ),
    inference(fof_simplification,[status(thm)],[fact_985_setsum_Oinfinite]) ).

fof(i_0_1430,plain,
    ! [X1,X2] :
      ( comm_monoid_add(X2)
     => ! [X38,X40] :
          ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
         => hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),big_co1399186613setsum(X1,X2),X38),X40) = zero_zero(X2) ) ),
    inference(fof_simplification,[status(thm)],[fact_984_setsum__infinite]) ).

fof(i_0_1431,plain,
    ! [X3844,X3845] : ti(fun(fun(product_prod(X3844,X3845),bool),fun(X3844,fun(X3845,bool))),in_rel(X3844,X3845)) = in_rel(X3844,X3845),
    inference(variable_rename,[status(thm)],[tsy_c_FunDef_Oin__rel_res]) ).

fof(i_0_1432,plain,
    ! [X7140,X7141] : hAPP(fun(X7140,bool),fun(X7140,bool),hAPP(fun(X7140,bool),fun(fun(X7140,bool),fun(X7140,bool)),semilattice_inf_inf(fun(X7140,bool)),X7141),top_top(fun(X7140,bool))) = ti(fun(X7140,bool),X7141),
    inference(variable_rename,[status(thm)],[fact_893_Int__UNIV__right]) ).

fof(i_0_1433,plain,
    ! [X119,X118] :
      ( ~ hBOOL(X118)
      | ~ hBOOL(X119)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X118),X119)) ),
    inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).

fof(i_0_1434,plain,
    ! [X119,X118] :
      ( ~ hBOOL(X118)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).

fof(i_0_1435,plain,
    ! [X118,X119] :
      ( ~ hBOOL(X119)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X118),X119)) ),
    inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).

fof(i_0_1436,plain,
    ! [X3895,X3896] : ti(fun(fun(X3895,X3896),fun(fun(X3895,bool),fun(X3896,bool))),image(X3895,X3896)) = image(X3895,X3896),
    inference(variable_rename,[status(thm)],[tsy_c_Set_Oimage_res]) ).

fof(i_0_1437,plain,
    ! [X5240,X5241] :
      ( ( hAPP(X5240,X5240,hAPP(X5240,fun(X5240,X5240),plus_plus(X5240),X5241),X5241) != zero_zero(X5240)
        | ti(X5240,X5241) = zero_zero(X5240)
        | ~ linord219039673up_add(X5240) )
      & ( ti(X5240,X5241) != zero_zero(X5240)
        | hAPP(X5240,X5240,hAPP(X5240,fun(X5240,X5240),plus_plus(X5240),X5241),X5241) = zero_zero(X5240)
        | ~ linord219039673up_add(X5240) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_double__eq__0__iff])])])]) ).

fof(i_0_1438,plain,
    ! [X5027,X5028] :
      ( ( zero_zero(X5027) != hAPP(X5027,X5027,hAPP(X5027,fun(X5027,X5027),plus_plus(X5027),X5028),X5028)
        | ti(X5027,X5028) = zero_zero(X5027)
        | ~ linord219039673up_add(X5027) )
      & ( ti(X5027,X5028) != zero_zero(X5027)
        | zero_zero(X5027) = hAPP(X5027,X5027,hAPP(X5027,fun(X5027,X5027),plus_plus(X5027),X5028),X5028)
        | ~ linord219039673up_add(X5027) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_double__zero__sym])])])]) ).

fof(i_0_1439,plain,
    ! [X6736,X6737] : hAPP(fun(X6736,bool),fun(X6736,bool),hAPP(fun(X6736,bool),fun(fun(X6736,bool),fun(X6736,bool)),semilattice_sup_sup(fun(X6736,bool)),X6737),X6737) = ti(fun(X6736,bool),X6737),
    inference(variable_rename,[status(thm)],[fact_791_Un__absorb]) ).

fof(i_0_1440,plain,
    ! [X7192,X7193] : hAPP(fun(X7192,bool),fun(X7192,bool),hAPP(fun(X7192,bool),fun(fun(X7192,bool),fun(X7192,bool)),semilattice_inf_inf(fun(X7192,bool)),X7193),X7193) = ti(fun(X7192,bool),X7193),
    inference(variable_rename,[status(thm)],[fact_908_Int__absorb]) ).

fof(i_0_1441,plain,
    ! [X5365,X5366] : hAPP(fun(X5365,bool),fun(X5365,bool),hAPP(fun(X5365,X5365),fun(fun(X5365,bool),fun(X5365,bool)),image(X5365,X5365),combi(X5365)),X5366) = ti(fun(X5365,bool),X5366),
    inference(variable_rename,[status(thm)],[fact_466_image__ident]) ).

fof(i_0_1442,plain,
    ! [X5695,X5696,X5697] :
      ( ( hAPP(X5695,fun(X5695,bool),ord_greaterThan(X5695),X5696) != hAPP(X5695,fun(X5695,bool),ord_greaterThan(X5695),X5697)
        | ti(X5695,X5696) = ti(X5695,X5697)
        | ~ linorder(X5695) )
      & ( ti(X5695,X5696) != ti(X5695,X5697)
        | hAPP(X5695,fun(X5695,bool),ord_greaterThan(X5695),X5696) = hAPP(X5695,fun(X5695,bool),ord_greaterThan(X5695),X5697)
        | ~ linorder(X5695) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_534_greaterThan__eq__iff])])])]) ).

fof(i_0_1443,plain,
    ! [X7014,X7015,X7016] :
      ( ( hAPP(X7014,fun(X7014,bool),ord_atLeast(X7014),X7015) != hAPP(X7014,fun(X7014,bool),ord_atLeast(X7014),X7016)
        | ti(X7014,X7015) = ti(X7014,X7016)
        | ~ linorder(X7014) )
      & ( ti(X7014,X7015) != ti(X7014,X7016)
        | hAPP(X7014,fun(X7014,bool),ord_atLeast(X7014),X7015) = hAPP(X7014,fun(X7014,bool),ord_atLeast(X7014),X7016)
        | ~ linorder(X7014) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_861_atLeast__eq__iff])])])]) ).

fof(i_0_1444,plain,
    ! [X3879] : ti(fun(X3879,fun(fun(nat,X3879),fun(nat,X3879))),nat_case(X3879)) = nat_case(X3879),
    inference(variable_rename,[status(thm)],[tsy_c_Nat_Onat_Onat__case_res]) ).

fof(i_0_1445,plain,
    ! [X3899] : ti(fun(product_prod(fun(X3899,bool),fun(X3899,bool)),bool),finite_psubset(X3899)) = finite_psubset(X3899),
    inference(variable_rename,[status(thm)],[tsy_c_Wellfounded_Ofinite__psubset_res]) ).

fof(i_0_1446,plain,
    ! [X3903,X3904,X3905,X3906] : hAPP(X3903,X3904,ti(fun(X3903,X3904),X3905),X3906) = hAPP(X3903,X3904,X3905,X3906),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).

fof(i_0_1447,plain,
    ! [X3820,X3821] :
      ( ~ comm_monoid_add(X3821)
      | ti(fun(fun(X3820,X3821),fun(fun(X3820,bool),X3821)),big_co1399186613setsum(X3820,X3821)) = big_co1399186613setsum(X3820,X3821) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res])]) ).

fof(i_0_1448,plain,
    ! [X3858,X3859] : ti(fun(fun(X3858,bool),fun(fun(X3858,X3859),bool)),extensional(X3858,X3859)) = extensional(X3858,X3859),
    inference(variable_rename,[status(thm)],[tsy_c_FuncSet_Oextensional_res]) ).

fof(i_0_1449,plain,
    ! [X3849,X3850] : ti(fun(fun(X3849,X3850),fun(fun(X3849,bool),bool)),inj_on(X3849,X3850)) = inj_on(X3849,X3850),
    inference(variable_rename,[status(thm)],[tsy_c_Fun_Oinj__on_res]) ).

fof(i_0_1450,plain,
    ! [X3900] : ti(fun(fun(X3900,nat),fun(product_prod(X3900,X3900),bool)),measure(X3900)) = measure(X3900),
    inference(variable_rename,[status(thm)],[tsy_c_Wellfounded_Omeasure_res]) ).

fof(i_0_1451,plain,
    ! [X7607,X7608,X7609,X7610] : hAPP(X7607,X7608,hAPP(X7608,fun(X7607,X7608),combk(X7608,X7607),X7609),X7610) = ti(X7608,X7609),
    inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).

fof(i_0_1452,plain,
    ! [X7294,X7295] :
      ( ~ bounded_lattice_top(X7294)
      | hAPP(X7294,X7294,hAPP(X7294,fun(X7294,X7294),semilattice_inf_inf(X7294),top_top(X7294)),X7295) = ti(X7294,X7295) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_936_inf__top__left])])]) ).

fof(i_0_1453,plain,
    ! [X5985,X5986] :
      ( ~ comm_monoid_mult(X5985)
      | hAPP(X5985,X5985,hAPP(X5985,fun(X5985,X5985),times_times(X5985),one_one(X5985)),X5986) = ti(X5985,X5986) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_613_mult__1])])]) ).

fof(i_0_1454,plain,
    ! [X5901,X5902] :
      ( ~ comm_semiring_1(X5901)
      | hAPP(X5901,X5901,hAPP(X5901,fun(X5901,X5901),times_times(X5901),one_one(X5901)),X5902) = ti(X5901,X5902) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])]) ).

fof(i_0_1455,plain,
    ! [X5983,X5984] :
      ( ~ monoid_mult(X5983)
      | hAPP(X5983,X5983,hAPP(X5983,fun(X5983,X5983),times_times(X5983),one_one(X5983)),X5984) = ti(X5983,X5984) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_612_mult__1__left])])]) ).

fof(i_0_1456,plain,
    ! [X5287,X5288] :
      ( ~ comm_semiring_1(X5287)
      | hAPP(X5287,X5287,hAPP(X5287,fun(X5287,X5287),plus_plus(X5287),zero_zero(X5287)),X5288) = ti(X5287,X5288) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).

fof(i_0_1457,plain,
    ! [X5031,X5032] :
      ( ~ monoid_add(X5031)
      | hAPP(X5031,X5031,hAPP(X5031,fun(X5031,X5031),plus_plus(X5031),zero_zero(X5031)),X5032) = ti(X5031,X5032) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_326_add__0__left])])]) ).

fof(i_0_1458,plain,
    ! [X5029,X5030] :
      ( ~ comm_monoid_add(X5029)
      | hAPP(X5029,X5029,hAPP(X5029,fun(X5029,X5029),plus_plus(X5029),zero_zero(X5029)),X5030) = ti(X5029,X5030) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_325_add__0])])]) ).

fof(i_0_1459,plain,
    ! [X7292,X7293] :
      ( ~ bounded_lattice_top(X7292)
      | hAPP(X7292,X7292,hAPP(X7292,fun(X7292,X7292),semilattice_inf_inf(X7292),X7293),top_top(X7292)) = ti(X7292,X7293) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_935_inf__top__right])])]) ).

fof(i_0_1460,plain,
    ! [X5989,X5990] :
      ( ~ comm_monoid_mult(X5989)
      | hAPP(X5989,X5989,hAPP(X5989,fun(X5989,X5989),times_times(X5989),X5990),one_one(X5989)) = ti(X5989,X5990) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_615_mult_Ocomm__neutral])])]) ).

fof(i_0_1461,plain,
    ! [X5899,X5900] :
      ( ~ comm_semiring_1(X5899)
      | hAPP(X5899,X5899,hAPP(X5899,fun(X5899,X5899),times_times(X5899),X5900),one_one(X5899)) = ti(X5899,X5900) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_582_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])]) ).

fof(i_0_1462,plain,
    ! [X5987,X5988] :
      ( ~ monoid_mult(X5987)
      | hAPP(X5987,X5987,hAPP(X5987,fun(X5987,X5987),times_times(X5987),X5988),one_one(X5987)) = ti(X5987,X5988) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_614_mult__1__right])])]) ).

fof(i_0_1463,plain,
    ! [X5316,X5317] :
      ( ~ comm_semiring_1(X5316)
      | hAPP(X5316,X5316,hAPP(X5316,fun(X5316,X5316),plus_plus(X5316),X5317),zero_zero(X5316)) = ti(X5316,X5317) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).

fof(i_0_1464,plain,
    ! [X5025,X5026] :
      ( ~ monoid_add(X5025)
      | hAPP(X5025,X5025,hAPP(X5025,fun(X5025,X5025),plus_plus(X5025),X5026),zero_zero(X5025)) = ti(X5025,X5026) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_323_add__0__right])])]) ).

fof(i_0_1465,plain,
    ! [X5023,X5024] :
      ( ~ comm_monoid_add(X5023)
      | hAPP(X5023,X5023,hAPP(X5023,fun(X5023,X5023),plus_plus(X5023),X5024),zero_zero(X5023)) = ti(X5023,X5024) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_322_add_Ocomm__neutral])])]) ).

fof(i_0_1466,plain,
    ! [X7455,X7456] :
      ( ~ lattice(X7455)
      | hAPP(X7455,X7455,hAPP(X7455,fun(X7455,X7455),semilattice_sup_sup(X7455),X7456),X7456) = ti(X7455,X7456) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_976_Sup__fin_Oidem])])]) ).

fof(i_0_1467,plain,
    ! [X6875,X6876] :
      ( ~ semilattice_sup(X6875)
      | hAPP(X6875,X6875,hAPP(X6875,fun(X6875,X6875),semilattice_sup_sup(X6875),X6876),X6876) = ti(X6875,X6876) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_823_sup__idem])])]) ).

fof(i_0_1468,plain,
    ! [X6873,X6874] :
      ( ~ semilattice_sup(X6873)
      | hAPP(X6873,X6873,hAPP(X6873,fun(X6873,X6873),semilattice_sup_sup(X6873),X6874),X6874) = ti(X6873,X6874) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_822_sup_Oidem])])]) ).

fof(i_0_1469,plain,
    ! [X7457,X7458] :
      ( ~ lattice(X7457)
      | hAPP(X7457,X7457,hAPP(X7457,fun(X7457,X7457),semilattice_inf_inf(X7457),X7458),X7458) = ti(X7457,X7458) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_977_Inf__fin_Oidem])])]) ).

fof(i_0_1470,plain,
    ! [X7350,X7351] :
      ( ~ semilattice_inf(X7350)
      | hAPP(X7350,X7350,hAPP(X7350,fun(X7350,X7350),semilattice_inf_inf(X7350),X7351),X7351) = ti(X7350,X7351) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_952_inf_Oidem])])]) ).

fof(i_0_1471,plain,
    ! [X7348,X7349] :
      ( ~ semilattice_inf(X7348)
      | hAPP(X7348,X7348,hAPP(X7348,fun(X7348,X7348),semilattice_inf_inf(X7348),X7349),X7349) = ti(X7348,X7349) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_951_inf__idem])])]) ).

fof(i_0_1472,plain,
    ! [X6868,X6869] :
      ( ~ ab_sem1668676832m_mult(X6868)
      | hAPP(X6868,X6868,hAPP(X6868,fun(X6868,X6868),times_times(X6868),X6869),X6869) = ti(X6868,X6869) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_820_mult__idem])])]) ).

fof(i_0_1473,plain,
    ! [X6866,X6867] :
      ( ~ ab_sem1668676832m_mult(X6866)
      | hAPP(X6866,X6866,hAPP(X6866,fun(X6866,X6866),times_times(X6866),X6867),X6867) = ti(X6866,X6867) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_819_times_Oidem])])]) ).

fof(i_0_1474,plain,
    ! [X3883,X3884] : ti(fun(X3883,fun(X3884,product_prod(X3883,X3884))),product_Pair(X3883,X3884)) = product_Pair(X3883,X3884),
    inference(variable_rename,[status(thm)],[tsy_c_Product__Type_OPair_res]) ).

fof(i_0_1475,plain,
    ! [X7582,X7583] : ti(X7582,ti(X7582,X7583)) = ti(X7582,X7583),
    inference(variable_rename,[status(thm)],[help_ti_idem]) ).

fof(i_0_1476,plain,
    ! [X3907,X3908,X3909,X3910] : hAPP(X3907,X3908,X3909,ti(X3907,X3910)) = hAPP(X3907,X3908,X3909,X3910),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).

fof(i_0_1477,plain,
    ! [X3911,X3912,X3913,X3914] : ti(X3911,hAPP(X3912,X3911,X3913,X3914)) = hAPP(X3912,X3911,X3913,X3914),
    inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).

fof(i_0_1478,plain,
    ! [X3875] : ti(fun(bool,fun(X3875,fun(X3875,X3875))),if(X3875)) = if(X3875),
    inference(variable_rename,[status(thm)],[tsy_c_If_res]) ).

fof(i_0_1479,plain,
    ! [X3893] :
      ( ~ linorder(X3893)
      | ti(fun(X3893,fun(X3893,fun(X3893,bool))),ord_gr676655987ssThan(X3893)) = ord_gr676655987ssThan(X3893) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_res])]) ).

fof(i_0_1480,plain,
    ! [X3892] :
      ( ~ linorder(X3892)
      | ti(fun(X3892,fun(X3892,fun(X3892,bool))),ord_gr1471790799AtMost(X3892)) = ord_gr1471790799AtMost(X3892) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThanAtMost_res])]) ).

fof(i_0_1481,plain,
    ! [X3890] :
      ( ~ linorder(X3890)
      | ti(fun(X3890,fun(X3890,fun(X3890,bool))),ord_atLeastLessThan(X3890)) = ord_atLeastLessThan(X3890) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeastLessThan_res])]) ).

fof(i_0_1482,plain,
    ! [X3889] :
      ( ~ order(X3889)
      | ti(fun(X3889,fun(X3889,fun(X3889,bool))),ord_atLeastAtMost(X3889)) = ord_atLeastAtMost(X3889) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeastAtMost_res])]) ).

fof(i_0_1483,plain,
    ! [X3916] : ti(fun(X3916,fun(fun(X3916,bool),bool)),member(X3916)) = member(X3916),
    inference(variable_rename,[status(thm)],[tsy_c_member_res]) ).

fof(i_0_1484,plain,
    ! [X1,X40] :
      ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X40))
     => hAPP(fun(X1,bool),nat,finite_card(X1),X40) = zero_zero(nat) ),
    inference(fof_simplification,[status(thm)],[fact_357_card__infinite]) ).

fof(i_0_1485,hypothesis,
    ! [X3915] :
      ( ( ~ hBOOL(ti(bool,X3915))
        | hBOOL(X3915) )
      & ( ~ hBOOL(X3915)
        | hBOOL(ti(bool,X3915)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])]) ).

fof(i_0_1486,plain,
    ! [X118] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X118))
      | ~ hBOOL(X118) ),
    inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).

fof(i_0_1487,plain,
    ! [X3894] : ti(fun(fun(X3894,bool),fun(X3894,bool)),collect(X3894)) = collect(X3894),
    inference(variable_rename,[status(thm)],[tsy_c_Set_OCollect_res]) ).

fof(i_0_1488,plain,
    ! [X4129,X4130] : hAPP(fun(X4129,bool),fun(X4129,bool),collect(X4129),X4130) = ti(fun(X4129,bool),X4130),
    inference(variable_rename,[status(thm)],[fact_77_Collect__def]) ).

fof(i_0_1489,plain,
    ! [X3829,X3830] : ti(fun(X3829,fun(X3830,X3829)),combk(X3829,X3830)) = combk(X3829,X3830),
    inference(variable_rename,[status(thm)],[tsy_c_COMBK_res]) ).

fof(i_0_1490,plain,
    ! [X3878] :
      ( ~ semilattice_sup(X3878)
      | ti(fun(X3878,fun(X3878,X3878)),semilattice_sup_sup(X3878)) = semilattice_sup_sup(X3878) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Lattices_Osemilattice__sup__class_Osup_res])]) ).

fof(i_0_1491,plain,
    ! [X3877] :
      ( ~ semilattice_inf(X3877)
      | ti(fun(X3877,fun(X3877,X3877)),semilattice_inf_inf(X3877)) = semilattice_inf_inf(X3877) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Lattices_Osemilattice__inf__class_Oinf_res])]) ).

fof(i_0_1492,plain,
    ! [X3870] :
      ( ~ no_zero_divisors(X3870)
      | ti(fun(X3870,fun(X3870,X3870)),times_times(X3870)) = times_times(X3870) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_4_res])]) ).

fof(i_0_1493,plain,
    ! [X3869] :
      ( ~ mult_zero(X3869)
      | ti(fun(X3869,fun(X3869,X3869)),times_times(X3869)) = times_times(X3869) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_3_res])]) ).

fof(i_0_1494,plain,
    ! [X3868] :
      ( ~ ab_semigroup_mult(X3868)
      | ti(fun(X3868,fun(X3868,X3868)),times_times(X3868)) = times_times(X3868) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_2_res])]) ).

fof(i_0_1495,plain,
    ! [X3867] :
      ( ~ monoid_mult(X3867)
      | ti(fun(X3867,fun(X3867,X3867)),times_times(X3867)) = times_times(X3867) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_1_res])]) ).

fof(i_0_1496,plain,
    ! [X3866] :
      ( ~ semiring(X3866)
      | ti(fun(X3866,fun(X3866,X3866)),times_times(X3866)) = times_times(X3866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Otimes__class_Otimes_0_res])]) ).

fof(i_0_1497,plain,
    ! [X3865] :
      ( ~ cancel_semigroup_add(X3865)
      | ti(fun(X3865,fun(X3865,X3865)),plus_plus(X3865)) = plus_plus(X3865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res])]) ).

fof(i_0_1498,plain,
    ! [X3864] :
      ( ~ ab_semigroup_add(X3864)
      | ti(fun(X3864,fun(X3864,X3864)),plus_plus(X3864)) = plus_plus(X3864) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res])]) ).

fof(i_0_1499,plain,
    ! [X3863] :
      ( ~ monoid_add(X3863)
      | ti(fun(X3863,fun(X3863,X3863)),plus_plus(X3863)) = plus_plus(X3863) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res])]) ).

fof(i_0_1500,plain,
    ! [X3891] :
      ( ~ ord(X3891)
      | ti(fun(X3891,fun(X3891,bool)),ord_greaterThan(X3891)) = ord_greaterThan(X3891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OgreaterThan_res])]) ).

fof(i_0_1501,plain,
    ! [X3888] :
      ( ~ ord(X3888)
      | ti(fun(X3888,fun(X3888,bool)),ord_atLeast(X3888)) = ord_atLeast(X3888) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_SetInterval_Oord__class_OatLeast_res])]) ).

fof(i_0_1502,plain,
    ! [X3881] :
      ( ~ ord(X3881)
      | ti(fun(X3881,fun(X3881,bool)),ord_less_eq(X3881)) = ord_less_eq(X3881) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res])]) ).

fof(i_0_1503,plain,
    ! [X3880] :
      ( ~ ord(X3880)
      | ti(fun(X3880,fun(X3880,bool)),ord_less(X3880)) = ord_less(X3880) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res])]) ).

fof(i_0_1504,plain,
    ! [X3902] : ti(fun(X3902,fun(X3902,bool)),fequal(X3902)) = fequal(X3902),
    inference(variable_rename,[status(thm)],[tsy_c_fequal_res]) ).

fof(i_0_1505,plain,
    ! [X3834] : ti(fun(fun(X3834,bool),nat),finite_card(X3834)) = finite_card(X3834),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).

fof(i_0_1506,plain,
    ! [X3835] : ti(fun(fun(X3835,bool),bool),finite_finite_1(X3835)) = finite_finite_1(X3835),
    inference(variable_rename,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).

fof(i_0_1507,plain,
    ! [X7630] :
      ( ti(bool,X7630) = fTrue
      | ti(bool,X7630) = fFalse ),
    inference(variable_rename,[status(thm)],[help_fFalse_1_1_T]) ).

fof(i_0_1508,plain,
    ! [X7617] :
      ( ti(bool,X7617) = fTrue
      | ti(bool,X7617) = fFalse ),
    inference(variable_rename,[status(thm)],[help_fTrue_1_1_T]) ).

fof(i_0_1509,plain,
    ! [X7590] :
      ( ti(bool,X7590) = fTrue
      | ti(bool,X7590) = fFalse ),
    inference(variable_rename,[status(thm)],[help_If_3_1_T]) ).

fof(i_0_1510,plain,
    ! [X3828] : ti(fun(X3828,X3828),combi(X3828)) = combi(X3828),
    inference(variable_rename,[status(thm)],[tsy_c_COMBI_res]) ).

fof(i_0_1511,plain,
    ! [X3876] :
      ( ~ ring_1(X3876)
      | ti(fun(X3876,bool),ring_1_Ints(X3876)) = ring_1_Ints(X3876) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Int_Oring__1__class_OInts_res])]) ).

fof(i_0_1512,plain,
    ! [X3882] :
      ( ~ top(X3882)
      | ti(X3882,top_top(X3882)) = top_top(X3882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Otop__class_Otop_res])]) ).

fof(i_0_1513,plain,
    ! [X3871] :
      ( ~ zero(X3871)
      | ti(X3871,zero_zero(X3871)) = zero_zero(X3871) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res])]) ).

fof(i_0_1514,plain,
    ! [X3862] :
      ( ~ one(X3862)
      | ti(X3862,one_one(X3862)) = one_one(X3862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res])]) ).

fof(i_0_1515,plain,
    ! [X3872] : ti(X3872,undefined(X3872)) = undefined(X3872),
    inference(variable_rename,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).

cnf(i_0_1516,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X5),X8) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X4),X7)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X7))
    | hAPP(X1,X1,X6,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != ti(X1,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | hAPP(X1,X3,X4,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X3,X5,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X6,esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X8))
    | hAPP(X1,X1,X2,hAPP(X1,X1,X6,esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != ti(X1,esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool,hAPP(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool)),finite_folding_image(X3,X1),X9),X10),X11)) ),
    inference(split_conjunct,[status(thm)],[i_0_1179]) ).

cnf(i_0_1517,plain,
    hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1180]) ).

cnf(i_0_1518,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X5),X8) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X4),X7)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11)),X7))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X7))
    | hAPP(X1,X1,X6,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != ti(X1,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | hAPP(X1,X3,X4,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X3,X5,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool,hAPP(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool)),finite_folding_image(X3,X1),X9),X10),X11)) ),
    inference(split_conjunct,[status(thm)],[i_0_1179]) ).

cnf(i_0_1519,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)),X8))
    | hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X4),X8) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X3),X7)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X6,esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))),X8))
    | hAPP(X1,X1,X5,hAPP(X1,X1,X6,esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))) != ti(X1,esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X9),X10),X11)) ),
    inference(split_conjunct,[status(thm)],[i_0_1179]) ).

cnf(i_0_1520,plain,
    ( hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10) = hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9))
    | hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X2,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X8,esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X10))
    | hAPP(X2,X1,X3,hAPP(X1,X2,X8,esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X1,esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X10))
    | ~ comm_monoid_mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1181]) ).

cnf(i_0_1521,plain,
    ( hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10) = hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10)),X9))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9))
    | hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != ti(X2,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X10))
    | ~ comm_monoid_mult(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1181]) ).

cnf(i_0_1522,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk144_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
    | hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X8,esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))),X10))
    | hAPP(X1,X2,X7,hAPP(X2,X1,X8,esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))) != ti(X2,esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X10))
    | ~ comm_monoid_mult(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1181]) ).

fof(i_0_1523,plain,
    ! [X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601] :
      ( ( hBOOL(hAPP(fun(X6593,bool),bool,hAPP(X6593,fun(fun(X6593,bool),bool),member(X6593),esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,esk157_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk159_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) )
      & ( ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(X6593,X6594,X6595,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))),hAPP(X6593,X6594,X6596,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,esk157_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk159_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) )
      & ( hBOOL(hAPP(fun(X6593,bool),bool,hAPP(X6593,fun(fun(X6593,bool),bool),member(X6593),esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,esk158_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk160_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) )
      & ( ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(X6593,X6594,X6595,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))),hAPP(X6593,X6594,X6596,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,esk158_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk160_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) )
      & ( hBOOL(hAPP(fun(X6593,bool),bool,hAPP(X6593,fun(fun(X6593,bool),bool),member(X6593),esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),X6597))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(X6594,X6594,hAPP(X6594,fun(X6594,X6594),X6599,esk157_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk158_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))),hAPP(X6594,X6594,hAPP(X6594,fun(X6594,X6594),X6599,esk159_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk160_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) )
      & ( ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(X6593,X6594,X6595,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))),hAPP(X6593,X6594,X6596,esk161_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))))
        | hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6595),X6597)),hAPP(fun(X6593,bool),X6594,hAPP(fun(X6593,X6594),fun(fun(X6593,bool),X6594),X6601,X6596),X6597)))
        | ~ hBOOL(hAPP(fun(X6593,bool),bool,finite_finite_1(X6593),X6597))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,hAPP(X6594,X6594,hAPP(X6594,fun(X6594,X6594),X6599,esk157_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk158_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))),hAPP(X6594,X6594,hAPP(X6594,fun(X6594,X6594),X6599,esk159_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601)),esk160_9(X6593,X6594,X6595,X6596,X6597,X6598,X6599,X6600,X6601))))
        | ~ hBOOL(hAPP(X6594,bool,hAPP(X6594,fun(X6594,bool),X6598,X6600),X6600))
        | ~ hBOOL(hAPP(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool,hAPP(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool),hAPP(fun(X6594,fun(X6594,X6594)),fun(X6594,fun(fun(fun(X6593,X6594),fun(fun(X6593,bool),X6594)),bool)),finite_folding_image(X6594,X6593),X6599),X6600),X6601)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_758_folding__image_Orelated])])])]) ).

fof(i_0_1524,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_83__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk]) ).

fof(i_0_1525,plain,
    ( ( ~ 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i,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_1526,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_214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)
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ) ),
    inference(fof_nnf,[status(thm)],[fact_14_PW]) ).

fof(i_0_1527,plain,
    ! [X6860,X6861,X6862,X6863,X6864,X6865] :
      ( ( ~ hBOOL(hAPP(X6860,bool,hAPP(X6861,fun(X6860,bool),hAPP(fun(X6861,fun(X6860,bool)),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,bool)),fun(fun(X6861,fun(X6860,bool)),fun(X6861,fun(X6860,bool))),semilattice_sup_sup(fun(X6861,fun(X6860,bool))),hAPP(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool))),combc(X6861,fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),hAPP(fun(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)))),combb(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),X6861),combc(X6860,fun(product_prod(X6861,X6860),bool),bool)),hAPP(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),hAPP(fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)))),combb(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),X6861),hAPP(fun(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),combb(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),X6860),member(product_prod(X6861,X6860)))),product_Pair(X6861,X6860)))),X6862)),hAPP(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool))),combc(X6861,fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),hAPP(fun(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)))),combb(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),X6861),combc(X6860,fun(product_prod(X6861,X6860),bool),bool)),hAPP(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),hAPP(fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)))),combb(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),X6861),hAPP(fun(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),combb(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),X6860),member(product_prod(X6861,X6860)))),product_Pair(X6861,X6860)))),X6863)),X6864),X6865))
        | hBOOL(hAPP(fun(product_prod(X6861,X6860),bool),bool,hAPP(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),member(product_prod(X6861,X6860)),hAPP(X6860,product_prod(X6861,X6860),hAPP(X6861,fun(X6860,product_prod(X6861,X6860)),product_Pair(X6861,X6860),X6864),X6865)),hAPP(fun(product_prod(X6861,X6860),bool),fun(product_prod(X6861,X6860),bool),hAPP(fun(product_prod(X6861,X6860),bool),fun(fun(product_prod(X6861,X6860),bool),fun(product_prod(X6861,X6860),bool)),semilattice_sup_sup(fun(product_prod(X6861,X6860),bool)),X6862),X6863))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X6861,X6860),bool),bool,hAPP(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),member(product_prod(X6861,X6860)),hAPP(X6860,product_prod(X6861,X6860),hAPP(X6861,fun(X6860,product_prod(X6861,X6860)),product_Pair(X6861,X6860),X6864),X6865)),hAPP(fun(product_prod(X6861,X6860),bool),fun(product_prod(X6861,X6860),bool),hAPP(fun(product_prod(X6861,X6860),bool),fun(fun(product_prod(X6861,X6860),bool),fun(product_prod(X6861,X6860),bool)),semilattice_sup_sup(fun(product_prod(X6861,X6860),bool)),X6862),X6863)))
        | hBOOL(hAPP(X6860,bool,hAPP(X6861,fun(X6860,bool),hAPP(fun(X6861,fun(X6860,bool)),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,bool)),fun(fun(X6861,fun(X6860,bool)),fun(X6861,fun(X6860,bool))),semilattice_sup_sup(fun(X6861,fun(X6860,bool))),hAPP(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool))),combc(X6861,fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),hAPP(fun(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)))),combb(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),X6861),combc(X6860,fun(product_prod(X6861,X6860),bool),bool)),hAPP(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),hAPP(fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)))),combb(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),X6861),hAPP(fun(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),combb(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),X6860),member(product_prod(X6861,X6860)))),product_Pair(X6861,X6860)))),X6862)),hAPP(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool)),hAPP(fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(product_prod(X6861,X6860),bool),fun(X6861,fun(X6860,bool))),combc(X6861,fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),hAPP(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),hAPP(fun(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool))),fun(fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(X6861,fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)))),combb(fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(product_prod(X6861,X6860),bool),fun(X6860,bool)),X6861),combc(X6860,fun(product_prod(X6861,X6860),bool),bool)),hAPP(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),hAPP(fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),fun(fun(X6861,fun(X6860,product_prod(X6861,X6860))),fun(X6861,fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)))),combb(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool)),X6861),hAPP(fun(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool)),fun(fun(X6860,product_prod(X6861,X6860)),fun(X6860,fun(fun(product_prod(X6861,X6860),bool),bool))),combb(product_prod(X6861,X6860),fun(fun(product_prod(X6861,X6860),bool),bool),X6860),member(product_prod(X6861,X6860)))),product_Pair(X6861,X6860)))),X6863)),X6864),X6865)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_818_sup__Un__eq2])]) ).

fof(i_0_1528,plain,
    ! [X7417,X7418,X7419,X7420,X7421,X7422] :
      ( ( ~ hBOOL(hAPP(X7417,bool,hAPP(X7418,fun(X7417,bool),hAPP(fun(X7418,fun(X7417,bool)),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,bool)),fun(fun(X7418,fun(X7417,bool)),fun(X7418,fun(X7417,bool))),semilattice_inf_inf(fun(X7418,fun(X7417,bool))),hAPP(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool))),combc(X7418,fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),hAPP(fun(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)))),combb(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),X7418),combc(X7417,fun(product_prod(X7418,X7417),bool),bool)),hAPP(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),hAPP(fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)))),combb(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),X7418),hAPP(fun(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),combb(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),X7417),member(product_prod(X7418,X7417)))),product_Pair(X7418,X7417)))),X7419)),hAPP(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool))),combc(X7418,fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),hAPP(fun(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)))),combb(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),X7418),combc(X7417,fun(product_prod(X7418,X7417),bool),bool)),hAPP(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),hAPP(fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)))),combb(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),X7418),hAPP(fun(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),combb(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),X7417),member(product_prod(X7418,X7417)))),product_Pair(X7418,X7417)))),X7420)),X7421),X7422))
        | hBOOL(hAPP(fun(product_prod(X7418,X7417),bool),bool,hAPP(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),member(product_prod(X7418,X7417)),hAPP(X7417,product_prod(X7418,X7417),hAPP(X7418,fun(X7417,product_prod(X7418,X7417)),product_Pair(X7418,X7417),X7421),X7422)),hAPP(fun(product_prod(X7418,X7417),bool),fun(product_prod(X7418,X7417),bool),hAPP(fun(product_prod(X7418,X7417),bool),fun(fun(product_prod(X7418,X7417),bool),fun(product_prod(X7418,X7417),bool)),semilattice_inf_inf(fun(product_prod(X7418,X7417),bool)),X7419),X7420))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X7418,X7417),bool),bool,hAPP(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),member(product_prod(X7418,X7417)),hAPP(X7417,product_prod(X7418,X7417),hAPP(X7418,fun(X7417,product_prod(X7418,X7417)),product_Pair(X7418,X7417),X7421),X7422)),hAPP(fun(product_prod(X7418,X7417),bool),fun(product_prod(X7418,X7417),bool),hAPP(fun(product_prod(X7418,X7417),bool),fun(fun(product_prod(X7418,X7417),bool),fun(product_prod(X7418,X7417),bool)),semilattice_inf_inf(fun(product_prod(X7418,X7417),bool)),X7419),X7420)))
        | hBOOL(hAPP(X7417,bool,hAPP(X7418,fun(X7417,bool),hAPP(fun(X7418,fun(X7417,bool)),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,bool)),fun(fun(X7418,fun(X7417,bool)),fun(X7418,fun(X7417,bool))),semilattice_inf_inf(fun(X7418,fun(X7417,bool))),hAPP(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool))),combc(X7418,fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),hAPP(fun(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)))),combb(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),X7418),combc(X7417,fun(product_prod(X7418,X7417),bool),bool)),hAPP(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),hAPP(fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)))),combb(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),X7418),hAPP(fun(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),combb(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),X7417),member(product_prod(X7418,X7417)))),product_Pair(X7418,X7417)))),X7419)),hAPP(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool)),hAPP(fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(product_prod(X7418,X7417),bool),fun(X7418,fun(X7417,bool))),combc(X7418,fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),hAPP(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),hAPP(fun(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool))),fun(fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(X7418,fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)))),combb(fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(product_prod(X7418,X7417),bool),fun(X7417,bool)),X7418),combc(X7417,fun(product_prod(X7418,X7417),bool),bool)),hAPP(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),hAPP(fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),fun(fun(X7418,fun(X7417,product_prod(X7418,X7417))),fun(X7418,fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)))),combb(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool)),X7418),hAPP(fun(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool)),fun(fun(X7417,product_prod(X7418,X7417)),fun(X7417,fun(fun(product_prod(X7418,X7417),bool),bool))),combb(product_prod(X7418,X7417),fun(fun(product_prod(X7418,X7417),bool),bool),X7417),member(product_prod(X7418,X7417)))),product_Pair(X7418,X7417)))),X7420)),X7421),X7422)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_969_inf__Int__eq2])]) ).

fof(i_0_1529,plain,
    ! [X6317,X6318,X6319,X6320,X6321,X6322,X6323] :
      ( ( hBOOL(hAPP(fun(X6317,bool),bool,hAPP(X6317,fun(fun(X6317,bool),bool),member(X6317),esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,esk138_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk140_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) )
      & ( ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(X6317,X6318,X6319,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))),hAPP(X6317,X6318,X6320,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,esk138_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk140_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) )
      & ( hBOOL(hAPP(fun(X6317,bool),bool,hAPP(X6317,fun(fun(X6317,bool),bool),member(X6317),esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,esk139_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk141_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) )
      & ( ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(X6317,X6318,X6319,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))),hAPP(X6317,X6318,X6320,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,esk139_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk141_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) )
      & ( hBOOL(hAPP(fun(X6317,bool),bool,hAPP(X6317,fun(fun(X6317,bool),bool),member(X6317),esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),X6321))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(X6318,X6318,hAPP(X6318,fun(X6318,X6318),times_times(X6318),esk138_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk139_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))),hAPP(X6318,X6318,hAPP(X6318,fun(X6318,X6318),times_times(X6318),esk140_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk141_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) )
      & ( ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(X6317,X6318,X6319,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))),hAPP(X6317,X6318,X6320,esk142_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))))
        | hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6319),X6323),X6321)),hAPP(fun(X6317,bool),X6318,hAPP(X6318,fun(fun(X6317,bool),X6318),hAPP(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318)),hAPP(fun(X6318,fun(X6318,X6318)),fun(fun(X6317,X6318),fun(X6318,fun(fun(X6317,bool),X6318))),finite_fold_image(X6318,X6317),times_times(X6318)),X6320),X6323),X6321)))
        | ~ hBOOL(hAPP(fun(X6317,bool),bool,finite_finite_1(X6317),X6321))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,hAPP(X6318,X6318,hAPP(X6318,fun(X6318,X6318),times_times(X6318),esk138_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk139_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))),hAPP(X6318,X6318,hAPP(X6318,fun(X6318,X6318),times_times(X6318),esk140_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323)),esk141_7(X6317,X6318,X6319,X6320,X6321,X6322,X6323))))
        | ~ hBOOL(hAPP(X6318,bool,hAPP(X6318,fun(X6318,bool),X6322,X6323),X6323))
        | ~ comm_monoid_mult(X6318) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_709_fold__image__related])])])])]) ).

fof(i_0_1530,plain,
    ! [X4192] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4192),esk29_0))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X4192))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk29_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_1182])])])]) ).

fof(i_0_1531,plain,
    ! [X4190] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4190),esk28_0))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X4190))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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)],[fact_93__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_])])])]) ).

fof(i_0_1532,plain,
    ! [X4034] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4034),n))
      | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X4034))),lab)),lba)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_n_I2_J])]) ).

fof(i_0_1533,plain,
    ! [X4030] : hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X4030))),lab)),lba)),arrow_301600364e_Prof)),
    inference(variable_rename,[status(thm)],[fact_42_PiProf]) ).

fof(i_0_1534,plain,
    ! [X4461,X4462,X4463,X4464] :
      ( ( ~ hBOOL(hAPP(fun(X4461,fun(X4462,bool)),bool,hAPP(fun(X4461,fun(X4462,bool)),fun(fun(X4461,fun(X4462,bool)),bool),ord_less_eq(fun(X4461,fun(X4462,bool))),hAPP(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool)),hAPP(fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool))),combc(X4461,fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),hAPP(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),hAPP(fun(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)))),combb(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),X4461),combc(X4462,fun(product_prod(X4461,X4462),bool),bool)),hAPP(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),hAPP(fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)))),combb(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),X4461),hAPP(fun(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),combb(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool),X4462),member(product_prod(X4461,X4462)))),product_Pair(X4461,X4462)))),X4463)),hAPP(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool)),hAPP(fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool))),combc(X4461,fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),hAPP(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),hAPP(fun(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)))),combb(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),X4461),combc(X4462,fun(product_prod(X4461,X4462),bool),bool)),hAPP(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),hAPP(fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)))),combb(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),X4461),hAPP(fun(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),combb(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool),X4462),member(product_prod(X4461,X4462)))),product_Pair(X4461,X4462)))),X4464)))
        | hBOOL(hAPP(fun(product_prod(X4461,X4462),bool),bool,hAPP(fun(product_prod(X4461,X4462),bool),fun(fun(product_prod(X4461,X4462),bool),bool),ord_less_eq(fun(product_prod(X4461,X4462),bool)),X4463),X4464)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X4461,X4462),bool),bool,hAPP(fun(product_prod(X4461,X4462),bool),fun(fun(product_prod(X4461,X4462),bool),bool),ord_less_eq(fun(product_prod(X4461,X4462),bool)),X4463),X4464))
        | hBOOL(hAPP(fun(X4461,fun(X4462,bool)),bool,hAPP(fun(X4461,fun(X4462,bool)),fun(fun(X4461,fun(X4462,bool)),bool),ord_less_eq(fun(X4461,fun(X4462,bool))),hAPP(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool)),hAPP(fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool))),combc(X4461,fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),hAPP(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),hAPP(fun(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)))),combb(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),X4461),combc(X4462,fun(product_prod(X4461,X4462),bool),bool)),hAPP(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),hAPP(fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)))),combb(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),X4461),hAPP(fun(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),combb(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool),X4462),member(product_prod(X4461,X4462)))),product_Pair(X4461,X4462)))),X4463)),hAPP(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool)),hAPP(fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(product_prod(X4461,X4462),bool),fun(X4461,fun(X4462,bool))),combc(X4461,fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),hAPP(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),hAPP(fun(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool))),fun(fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(X4461,fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)))),combb(fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(product_prod(X4461,X4462),bool),fun(X4462,bool)),X4461),combc(X4462,fun(product_prod(X4461,X4462),bool),bool)),hAPP(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),hAPP(fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),fun(fun(X4461,fun(X4462,product_prod(X4461,X4462))),fun(X4461,fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)))),combb(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool)),X4461),hAPP(fun(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool)),fun(fun(X4462,product_prod(X4461,X4462)),fun(X4462,fun(fun(product_prod(X4461,X4462),bool),bool))),combb(product_prod(X4461,X4462),fun(fun(product_prod(X4461,X4462),bool),bool),X4462),member(product_prod(X4461,X4462)))),product_Pair(X4461,X4462)))),X4464))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_161_pred__subset__eq2])]) ).

fof(i_0_1535,plain,
    ! [X7133,X7134,X7135,X7136,X7137,X7138,X7139] :
      ( ~ comm_monoid_add(X7135)
      | ~ hBOOL(hAPP(fun(X7134,bool),bool,finite_finite_1(X7134),X7139))
      | ~ hBOOL(hAPP(fun(X7133,bool),bool,finite_finite_1(X7133),X7138))
      | hAPP(fun(X7134,bool),X7135,hAPP(fun(X7134,X7135),fun(fun(X7134,bool),X7135),big_co1399186613setsum(X7134,X7135),hAPP(fun(X7134,fun(X7133,bool)),fun(X7134,X7135),hAPP(fun(X7134,fun(fun(X7133,bool),X7135)),fun(fun(X7134,fun(X7133,bool)),fun(X7134,X7135)),combs(X7134,fun(X7133,bool),X7135),hAPP(fun(X7134,fun(X7133,X7135)),fun(X7134,fun(fun(X7133,bool),X7135)),hAPP(fun(fun(X7133,X7135),fun(fun(X7133,bool),X7135)),fun(fun(X7134,fun(X7133,X7135)),fun(X7134,fun(fun(X7133,bool),X7135))),combb(fun(X7133,X7135),fun(fun(X7133,bool),X7135),X7134),big_co1399186613setsum(X7133,X7135)),X7136)),hAPP(fun(X7134,fun(X7133,bool)),fun(X7134,fun(X7133,bool)),hAPP(fun(fun(X7133,bool),fun(X7133,bool)),fun(fun(X7134,fun(X7133,bool)),fun(X7134,fun(X7133,bool))),combb(fun(X7133,bool),fun(X7133,bool),X7134),collect(X7133)),hAPP(fun(X7134,fun(X7133,bool)),fun(X7134,fun(X7133,bool)),hAPP(fun(fun(X7133,bool),fun(X7133,bool)),fun(fun(X7134,fun(X7133,bool)),fun(X7134,fun(X7133,bool))),combb(fun(X7133,bool),fun(X7133,bool),X7134),hAPP(fun(X7133,fun(bool,bool)),fun(fun(X7133,bool),fun(X7133,bool)),combs(X7133,bool,bool),hAPP(fun(X7133,bool),fun(X7133,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7133,bool),fun(X7133,fun(bool,bool))),combb(bool,fun(bool,bool),X7133),fconj),hAPP(fun(X7133,bool),fun(X7133,bool),hAPP(fun(X7133,fun(fun(X7133,bool),bool)),fun(fun(X7133,bool),fun(X7133,bool)),combc(X7133,fun(X7133,bool),bool),member(X7133)),X7138)))),X7137)))),X7139) = hAPP(fun(X7133,bool),X7135,hAPP(fun(X7133,X7135),fun(fun(X7133,bool),X7135),big_co1399186613setsum(X7133,X7135),hAPP(fun(X7133,fun(X7134,bool)),fun(X7133,X7135),hAPP(fun(X7133,fun(fun(X7134,bool),X7135)),fun(fun(X7133,fun(X7134,bool)),fun(X7133,X7135)),combs(X7133,fun(X7134,bool),X7135),hAPP(fun(X7133,fun(X7134,X7135)),fun(X7133,fun(fun(X7134,bool),X7135)),hAPP(fun(fun(X7134,X7135),fun(fun(X7134,bool),X7135)),fun(fun(X7133,fun(X7134,X7135)),fun(X7133,fun(fun(X7134,bool),X7135))),combb(fun(X7134,X7135),fun(fun(X7134,bool),X7135),X7133),big_co1399186613setsum(X7134,X7135)),hAPP(fun(X7134,fun(X7133,X7135)),fun(X7133,fun(X7134,X7135)),combc(X7134,X7133,X7135),X7136))),hAPP(fun(X7133,fun(X7134,bool)),fun(X7133,fun(X7134,bool)),hAPP(fun(fun(X7134,bool),fun(X7134,bool)),fun(fun(X7133,fun(X7134,bool)),fun(X7133,fun(X7134,bool))),combb(fun(X7134,bool),fun(X7134,bool),X7133),collect(X7134)),hAPP(fun(X7133,fun(X7134,bool)),fun(X7133,fun(X7134,bool)),hAPP(fun(fun(X7134,bool),fun(X7134,bool)),fun(fun(X7133,fun(X7134,bool)),fun(X7133,fun(X7134,bool))),combb(fun(X7134,bool),fun(X7134,bool),X7133),hAPP(fun(X7134,fun(bool,bool)),fun(fun(X7134,bool),fun(X7134,bool)),combs(X7134,bool,bool),hAPP(fun(X7134,bool),fun(X7134,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7134,bool),fun(X7134,fun(bool,bool))),combb(bool,fun(bool,bool),X7134),fconj),hAPP(fun(X7134,bool),fun(X7134,bool),hAPP(fun(X7134,fun(fun(X7134,bool),bool)),fun(fun(X7134,bool),fun(X7134,bool)),combc(X7134,fun(X7134,bool),bool),member(X7134)),X7139)))),hAPP(fun(X7134,fun(X7133,bool)),fun(X7133,fun(X7134,bool)),combc(X7134,X7133,bool),X7137))))),X7138) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_892_setsum__setsum__restrict])])]) ).

fof(i_0_1536,plain,
    ! [X6526,X6527,X6528,X6529,X6530,X6531,X6532,X6533] :
      ( ( hBOOL(hAPP(fun(X6526,bool),bool,hAPP(X6526,fun(fun(X6526,bool),bool),member(X6526),esk152_8(X6526,X6527,X6528,X6529,X6530,X6531,X6532,X6533)),X6530))
        | hAPP(fun(X6526,bool),X6527,hAPP(fun(X6526,X6527),fun(fun(X6526,bool),X6527),X6533,X6528),X6530) = hAPP(fun(X6526,bool),X6527,hAPP(fun(X6526,X6527),fun(fun(X6526,bool),X6527),X6533,X6529),X6530)
        | ~ hBOOL(hAPP(fun(X6526,bool),bool,finite_finite_1(X6526),X6530))
        | ~ hBOOL(hAPP(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool,hAPP(X6527,fun(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool),hAPP(fun(X6527,fun(X6527,X6527)),fun(X6527,fun(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool)),finite_folding_image(X6527,X6526),X6531),X6532),X6533)) )
      & ( hAPP(X6526,X6527,X6528,esk152_8(X6526,X6527,X6528,X6529,X6530,X6531,X6532,X6533)) != hAPP(X6526,X6527,X6529,esk152_8(X6526,X6527,X6528,X6529,X6530,X6531,X6532,X6533))
        | hAPP(fun(X6526,bool),X6527,hAPP(fun(X6526,X6527),fun(fun(X6526,bool),X6527),X6533,X6528),X6530) = hAPP(fun(X6526,bool),X6527,hAPP(fun(X6526,X6527),fun(fun(X6526,bool),X6527),X6533,X6529),X6530)
        | ~ hBOOL(hAPP(fun(X6526,bool),bool,finite_finite_1(X6526),X6530))
        | ~ hBOOL(hAPP(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool,hAPP(X6527,fun(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool),hAPP(fun(X6527,fun(X6527,X6527)),fun(X6527,fun(fun(fun(X6526,X6527),fun(fun(X6526,bool),X6527)),bool)),finite_folding_image(X6527,X6526),X6531),X6532),X6533)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_745_folding__image_Ocong])])])]) ).

fof(i_0_1537,plain,
    ! [X7483,X7484,X7485,X7486,X7487,X7488,X7489] :
      ( ~ semiring_0(X7485)
      | hAPP(X7485,X7485,hAPP(X7485,fun(X7485,X7485),times_times(X7485),hAPP(fun(X7483,bool),X7485,hAPP(fun(X7483,X7485),fun(fun(X7483,bool),X7485),big_co1399186613setsum(X7483,X7485),X7486),X7487)),hAPP(fun(X7484,bool),X7485,hAPP(fun(X7484,X7485),fun(fun(X7484,bool),X7485),big_co1399186613setsum(X7484,X7485),X7488),X7489)) = hAPP(fun(X7483,bool),X7485,hAPP(fun(X7483,X7485),fun(fun(X7483,bool),X7485),big_co1399186613setsum(X7483,X7485),hAPP(fun(X7484,bool),fun(X7483,X7485),hAPP(fun(X7483,fun(fun(X7484,bool),X7485)),fun(fun(X7484,bool),fun(X7483,X7485)),combc(X7483,fun(X7484,bool),X7485),hAPP(fun(X7483,fun(X7484,X7485)),fun(X7483,fun(fun(X7484,bool),X7485)),hAPP(fun(fun(X7484,X7485),fun(fun(X7484,bool),X7485)),fun(fun(X7483,fun(X7484,X7485)),fun(X7483,fun(fun(X7484,bool),X7485))),combb(fun(X7484,X7485),fun(fun(X7484,bool),X7485),X7483),big_co1399186613setsum(X7484,X7485)),hAPP(fun(X7484,X7485),fun(X7483,fun(X7484,X7485)),hAPP(fun(X7483,fun(fun(X7484,X7485),fun(X7484,X7485))),fun(fun(X7484,X7485),fun(X7483,fun(X7484,X7485))),combc(X7483,fun(X7484,X7485),fun(X7484,X7485)),hAPP(fun(X7483,fun(X7485,X7485)),fun(X7483,fun(fun(X7484,X7485),fun(X7484,X7485))),hAPP(fun(fun(X7485,X7485),fun(fun(X7484,X7485),fun(X7484,X7485))),fun(fun(X7483,fun(X7485,X7485)),fun(X7483,fun(fun(X7484,X7485),fun(X7484,X7485)))),combb(fun(X7485,X7485),fun(fun(X7484,X7485),fun(X7484,X7485)),X7483),combb(X7485,X7485,X7484)),hAPP(fun(X7483,X7485),fun(X7483,fun(X7485,X7485)),hAPP(fun(X7485,fun(X7485,X7485)),fun(fun(X7483,X7485),fun(X7483,fun(X7485,X7485))),combb(X7485,fun(X7485,X7485),X7483),times_times(X7485)),X7486))),X7488))),X7489)),X7487) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_983_setsum__product])])]) ).

fof(i_0_1538,plain,
    ! [X5234,X5235] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5235))
      | 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)),X5235))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X5234))))) = 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)),X5235))),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,X5234))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_card__less__Suc])]) ).

fof(i_0_1539,plain,
    ! [X7127,X7128,X7129,X7130,X7131,X7132] :
      ( ~ comm_monoid_add(X7129)
      | ~ hBOOL(hAPP(fun(X7128,bool),bool,finite_finite_1(X7128),X7132))
      | hAPP(fun(X7128,bool),X7129,hAPP(fun(X7128,X7129),fun(fun(X7128,bool),X7129),big_co1399186613setsum(X7128,X7129),X7130),X7132) = hAPP(fun(X7127,bool),X7129,hAPP(fun(X7127,X7129),fun(fun(X7127,bool),X7129),big_co1399186613setsum(X7127,X7129),hAPP(fun(X7127,fun(X7128,bool)),fun(X7127,X7129),hAPP(fun(fun(X7128,bool),X7129),fun(fun(X7127,fun(X7128,bool)),fun(X7127,X7129)),combb(fun(X7128,bool),X7129,X7127),hAPP(fun(X7128,X7129),fun(fun(X7128,bool),X7129),big_co1399186613setsum(X7128,X7129),X7130)),hAPP(fun(X7127,fun(X7128,bool)),fun(X7127,fun(X7128,bool)),hAPP(fun(fun(X7128,bool),fun(X7128,bool)),fun(fun(X7127,fun(X7128,bool)),fun(X7127,fun(X7128,bool))),combb(fun(X7128,bool),fun(X7128,bool),X7127),collect(X7128)),hAPP(fun(X7127,fun(X7128,bool)),fun(X7127,fun(X7128,bool)),hAPP(fun(fun(X7128,bool),fun(X7128,bool)),fun(fun(X7127,fun(X7128,bool)),fun(X7127,fun(X7128,bool))),combb(fun(X7128,bool),fun(X7128,bool),X7127),hAPP(fun(X7128,fun(bool,bool)),fun(fun(X7128,bool),fun(X7128,bool)),combs(X7128,bool,bool),hAPP(fun(X7128,bool),fun(X7128,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7128,bool),fun(X7128,fun(bool,bool))),combb(bool,fun(bool,bool),X7128),fconj),hAPP(fun(X7128,bool),fun(X7128,bool),hAPP(fun(X7128,fun(fun(X7128,bool),bool)),fun(fun(X7128,bool),fun(X7128,bool)),combc(X7128,fun(X7128,bool),bool),member(X7128)),X7132)))),hAPP(fun(X7128,fun(X7127,bool)),fun(X7127,fun(X7128,bool)),combc(X7128,X7127,bool),hAPP(fun(X7128,X7127),fun(X7128,fun(X7127,bool)),hAPP(fun(X7127,fun(X7127,bool)),fun(fun(X7128,X7127),fun(X7128,fun(X7127,bool))),combb(X7127,fun(X7127,bool),X7128),fequal(X7127)),X7131)))))),hAPP(fun(X7128,bool),fun(X7127,bool),hAPP(fun(X7128,X7127),fun(fun(X7128,bool),fun(X7127,bool)),image(X7128,X7127),X7131),X7132)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_891_setsum__image__gen])])]) ).

fof(i_0_1540,plain,
    ! [X7225,X7226,X7227,X7228,X7229] :
      ( ~ comm_monoid_add(X7226)
      | ~ hBOOL(hAPP(fun(X7225,bool),bool,finite_finite_1(X7225),X7229))
      | hAPP(fun(X7225,bool),X7226,hAPP(fun(X7225,X7226),fun(fun(X7225,bool),X7226),big_co1399186613setsum(X7225,X7226),X7227),hAPP(fun(X7225,bool),fun(X7225,bool),collect(X7225),hAPP(fun(X7225,bool),fun(X7225,bool),hAPP(fun(X7225,fun(bool,bool)),fun(fun(X7225,bool),fun(X7225,bool)),combs(X7225,bool,bool),hAPP(fun(X7225,bool),fun(X7225,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7225,bool),fun(X7225,fun(bool,bool))),combb(bool,fun(bool,bool),X7225),fconj),hAPP(fun(X7225,bool),fun(X7225,bool),hAPP(fun(X7225,fun(fun(X7225,bool),bool)),fun(fun(X7225,bool),fun(X7225,bool)),combc(X7225,fun(X7225,bool),bool),member(X7225)),X7229))),hAPP(fun(X7225,bool),fun(X7225,bool),hAPP(fun(X7225,fun(fun(X7225,bool),bool)),fun(fun(X7225,bool),fun(X7225,bool)),combc(X7225,fun(X7225,bool),bool),member(X7225)),X7228)))) = hAPP(fun(X7225,bool),X7226,hAPP(fun(X7225,X7226),fun(fun(X7225,bool),X7226),big_co1399186613setsum(X7225,X7226),hAPP(X7226,fun(X7225,X7226),hAPP(fun(X7225,fun(X7226,X7226)),fun(X7226,fun(X7225,X7226)),combc(X7225,X7226,X7226),hAPP(fun(X7225,X7226),fun(X7225,fun(X7226,X7226)),hAPP(fun(X7225,fun(X7226,fun(X7226,X7226))),fun(fun(X7225,X7226),fun(X7225,fun(X7226,X7226))),combs(X7225,X7226,fun(X7226,X7226)),hAPP(fun(X7225,bool),fun(X7225,fun(X7226,fun(X7226,X7226))),hAPP(fun(bool,fun(X7226,fun(X7226,X7226))),fun(fun(X7225,bool),fun(X7225,fun(X7226,fun(X7226,X7226)))),combb(bool,fun(X7226,fun(X7226,X7226)),X7225),if(X7226)),hAPP(fun(X7225,bool),fun(X7225,bool),hAPP(fun(X7225,fun(fun(X7225,bool),bool)),fun(fun(X7225,bool),fun(X7225,bool)),combc(X7225,fun(X7225,bool),bool),member(X7225)),X7228))),X7227)),zero_zero(X7226))),X7229) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_917_setsum__restrict__set_H])])]) ).

fof(i_0_1541,plain,
    ! [X5632,X5633,X5634,X5635] :
      ( ( hBOOL(hAPP(fun(X5633,bool),bool,hAPP(X5633,fun(fun(X5633,bool),bool),member(X5633),esk117_4(X5632,X5633,X5634,X5635)),X5635))
        | ~ hBOOL(hAPP(fun(X5632,bool),bool,finite_finite_1(X5632),hAPP(fun(X5633,bool),fun(X5632,bool),hAPP(fun(X5633,X5632),fun(fun(X5633,bool),fun(X5632,bool)),image(X5633,X5632),X5634),X5635)))
        | hBOOL(hAPP(fun(X5633,bool),bool,finite_finite_1(X5633),X5635)) )
      & ( ~ hBOOL(hAPP(fun(X5633,bool),bool,finite_finite_1(X5633),hAPP(fun(X5633,bool),fun(X5633,bool),collect(X5633),hAPP(fun(X5633,bool),fun(X5633,bool),hAPP(fun(X5633,fun(bool,bool)),fun(fun(X5633,bool),fun(X5633,bool)),combs(X5633,bool,bool),hAPP(fun(X5633,bool),fun(X5633,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X5633,bool),fun(X5633,fun(bool,bool))),combb(bool,fun(bool,bool),X5633),fconj),hAPP(fun(X5633,bool),fun(X5633,bool),hAPP(fun(X5633,fun(fun(X5633,bool),bool)),fun(fun(X5633,bool),fun(X5633,bool)),combc(X5633,fun(X5633,bool),bool),member(X5633)),X5635))),hAPP(X5632,fun(X5633,bool),hAPP(fun(X5633,fun(X5632,bool)),fun(X5632,fun(X5633,bool)),combc(X5633,X5632,bool),hAPP(fun(X5633,X5632),fun(X5633,fun(X5632,bool)),hAPP(fun(X5632,fun(X5632,bool)),fun(fun(X5633,X5632),fun(X5633,fun(X5632,bool))),combb(X5632,fun(X5632,bool),X5633),fequal(X5632)),X5634)),hAPP(X5633,X5632,X5634,esk117_4(X5632,X5633,X5634,X5635)))))))
        | ~ hBOOL(hAPP(fun(X5632,bool),bool,finite_finite_1(X5632),hAPP(fun(X5633,bool),fun(X5632,bool),hAPP(fun(X5633,X5632),fun(fun(X5633,bool),fun(X5632,bool)),image(X5633,X5632),X5634),X5635)))
        | hBOOL(hAPP(fun(X5633,bool),bool,finite_finite_1(X5633),X5635)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1183])])])]) ).

fof(i_0_1542,plain,
    ! [X5238,X5239] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5239))
      | 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)),X5239))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X5238)))) = 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)),X5239))),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,X5238))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1184])]) ).

fof(i_0_1543,plain,
    ! [X7540,X7541,X7542,X7543,X7544] :
      ( ~ comm_monoid_add(X7541)
      | ~ hBOOL(hAPP(fun(X7540,bool),bool,finite_finite_1(X7540),X7544))
      | hAPP(fun(X7540,bool),X7541,hAPP(fun(X7540,X7541),fun(fun(X7540,bool),X7541),big_co1399186613setsum(X7540,X7541),X7542),hAPP(fun(X7540,bool),fun(X7540,bool),hAPP(fun(X7540,bool),fun(fun(X7540,bool),fun(X7540,bool)),semilattice_inf_inf(fun(X7540,bool)),X7544),X7543)) = hAPP(fun(X7540,bool),X7541,hAPP(fun(X7540,X7541),fun(fun(X7540,bool),X7541),big_co1399186613setsum(X7540,X7541),hAPP(X7541,fun(X7540,X7541),hAPP(fun(X7540,fun(X7541,X7541)),fun(X7541,fun(X7540,X7541)),combc(X7540,X7541,X7541),hAPP(fun(X7540,X7541),fun(X7540,fun(X7541,X7541)),hAPP(fun(X7540,fun(X7541,fun(X7541,X7541))),fun(fun(X7540,X7541),fun(X7540,fun(X7541,X7541))),combs(X7540,X7541,fun(X7541,X7541)),hAPP(fun(X7540,bool),fun(X7540,fun(X7541,fun(X7541,X7541))),hAPP(fun(bool,fun(X7541,fun(X7541,X7541))),fun(fun(X7540,bool),fun(X7540,fun(X7541,fun(X7541,X7541)))),combb(bool,fun(X7541,fun(X7541,X7541)),X7540),if(X7541)),hAPP(fun(X7540,bool),fun(X7540,bool),hAPP(fun(X7540,fun(fun(X7540,bool),bool)),fun(fun(X7540,bool),fun(X7540,bool)),combc(X7540,fun(X7540,bool),bool),member(X7540)),X7543))),X7542)),zero_zero(X7541))),X7544) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_994_setsum__restrict__set])])]) ).

fof(i_0_1544,plain,
    ! [X7508,X7509,X7510,X7511,X7512] :
      ( ( ~ hBOOL(hAPP(fun(X7508,bool),bool,hAPP(X7508,fun(fun(X7508,bool),bool),member(X7508),X7511),X7512))
        | hAPP(fun(X7508,bool),X7509,hAPP(fun(X7508,X7509),fun(fun(X7508,bool),X7509),big_co1399186613setsum(X7508,X7509),hAPP(X7509,fun(X7508,X7509),hAPP(fun(X7508,fun(X7509,X7509)),fun(X7509,fun(X7508,X7509)),combc(X7508,X7509,X7509),hAPP(fun(X7508,X7509),fun(X7508,fun(X7509,X7509)),hAPP(fun(X7508,fun(X7509,fun(X7509,X7509))),fun(fun(X7508,X7509),fun(X7508,fun(X7509,X7509))),combs(X7508,X7509,fun(X7509,X7509)),hAPP(fun(X7508,bool),fun(X7508,fun(X7509,fun(X7509,X7509))),hAPP(fun(bool,fun(X7509,fun(X7509,X7509))),fun(fun(X7508,bool),fun(X7508,fun(X7509,fun(X7509,X7509)))),combb(bool,fun(X7509,fun(X7509,X7509)),X7508),if(X7509)),hAPP(X7508,fun(X7508,bool),hAPP(fun(X7508,fun(X7508,bool)),fun(X7508,fun(X7508,bool)),combc(X7508,X7508,bool),fequal(X7508)),X7511))),X7510)),zero_zero(X7509))),X7512) = hAPP(X7508,X7509,X7510,X7511)
        | ~ hBOOL(hAPP(fun(X7508,bool),bool,finite_finite_1(X7508),X7512))
        | ~ comm_monoid_add(X7509) )
      & ( hBOOL(hAPP(fun(X7508,bool),bool,hAPP(X7508,fun(fun(X7508,bool),bool),member(X7508),X7511),X7512))
        | hAPP(fun(X7508,bool),X7509,hAPP(fun(X7508,X7509),fun(fun(X7508,bool),X7509),big_co1399186613setsum(X7508,X7509),hAPP(X7509,fun(X7508,X7509),hAPP(fun(X7508,fun(X7509,X7509)),fun(X7509,fun(X7508,X7509)),combc(X7508,X7509,X7509),hAPP(fun(X7508,X7509),fun(X7508,fun(X7509,X7509)),hAPP(fun(X7508,fun(X7509,fun(X7509,X7509))),fun(fun(X7508,X7509),fun(X7508,fun(X7509,X7509))),combs(X7508,X7509,fun(X7509,X7509)),hAPP(fun(X7508,bool),fun(X7508,fun(X7509,fun(X7509,X7509))),hAPP(fun(bool,fun(X7509,fun(X7509,X7509))),fun(fun(X7508,bool),fun(X7508,fun(X7509,fun(X7509,X7509)))),combb(bool,fun(X7509,fun(X7509,X7509)),X7508),if(X7509)),hAPP(X7508,fun(X7508,bool),hAPP(fun(X7508,fun(X7508,bool)),fun(X7508,fun(X7508,bool)),combc(X7508,X7508,bool),fequal(X7508)),X7511))),X7510)),zero_zero(X7509))),X7512) = zero_zero(X7509)
        | ~ hBOOL(hAPP(fun(X7508,bool),bool,finite_finite_1(X7508),X7512))
        | ~ comm_monoid_add(X7509) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1185])])])]) ).

fof(i_0_1545,plain,
    ! [X7220,X7221,X7222,X7223,X7224] :
      ( ~ comm_monoid_add(X7221)
      | ~ hBOOL(hAPP(fun(X7220,bool),bool,finite_finite_1(X7220),X7224))
      | hAPP(fun(X7220,bool),X7221,hAPP(fun(X7220,X7221),fun(fun(X7220,bool),X7221),big_co1399186613setsum(X7220,X7221),X7222),hAPP(fun(X7220,bool),fun(X7220,bool),collect(X7220),hAPP(fun(X7220,bool),fun(X7220,bool),hAPP(fun(X7220,fun(bool,bool)),fun(fun(X7220,bool),fun(X7220,bool)),combs(X7220,bool,bool),hAPP(fun(X7220,bool),fun(X7220,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7220,bool),fun(X7220,fun(bool,bool))),combb(bool,fun(bool,bool),X7220),fconj),hAPP(fun(X7220,bool),fun(X7220,bool),hAPP(fun(X7220,fun(fun(X7220,bool),bool)),fun(fun(X7220,bool),fun(X7220,bool)),combc(X7220,fun(X7220,bool),bool),member(X7220)),X7224))),X7223))) = hAPP(fun(X7220,bool),X7221,hAPP(fun(X7220,X7221),fun(fun(X7220,bool),X7221),big_co1399186613setsum(X7220,X7221),hAPP(X7221,fun(X7220,X7221),hAPP(fun(X7220,fun(X7221,X7221)),fun(X7221,fun(X7220,X7221)),combc(X7220,X7221,X7221),hAPP(fun(X7220,X7221),fun(X7220,fun(X7221,X7221)),hAPP(fun(X7220,fun(X7221,fun(X7221,X7221))),fun(fun(X7220,X7221),fun(X7220,fun(X7221,X7221))),combs(X7220,X7221,fun(X7221,X7221)),hAPP(fun(X7220,bool),fun(X7220,fun(X7221,fun(X7221,X7221))),hAPP(fun(bool,fun(X7221,fun(X7221,X7221))),fun(fun(X7220,bool),fun(X7220,fun(X7221,fun(X7221,X7221)))),combb(bool,fun(X7221,fun(X7221,X7221)),X7220),if(X7221)),X7223)),X7222)),zero_zero(X7221))),X7224) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_916_setsum__restrict__set_H_H])])]) ).

fof(i_0_1546,plain,
    ! [X7107,X7108,X7109,X7110,X7111,X7112] : hAPP(fun(X7107,bool),fun(X7108,bool),hAPP(fun(X7107,X7108),fun(fun(X7107,bool),fun(X7108,bool)),image(X7107,X7108),hAPP(fun(X7107,X7108),fun(X7107,X7108),hAPP(fun(X7107,fun(X7108,X7108)),fun(fun(X7107,X7108),fun(X7107,X7108)),combs(X7107,X7108,X7108),hAPP(fun(X7107,X7108),fun(X7107,fun(X7108,X7108)),hAPP(fun(X7107,fun(X7108,fun(X7108,X7108))),fun(fun(X7107,X7108),fun(X7107,fun(X7108,X7108))),combs(X7107,X7108,fun(X7108,X7108)),hAPP(fun(X7107,bool),fun(X7107,fun(X7108,fun(X7108,X7108))),hAPP(fun(bool,fun(X7108,fun(X7108,X7108))),fun(fun(X7107,bool),fun(X7107,fun(X7108,fun(X7108,X7108)))),combb(bool,fun(X7108,fun(X7108,X7108)),X7107),if(X7108)),X7109)),X7110)),X7111)),X7112) = hAPP(fun(X7108,bool),fun(X7108,bool),hAPP(fun(X7108,bool),fun(fun(X7108,bool),fun(X7108,bool)),semilattice_sup_sup(fun(X7108,bool)),hAPP(fun(X7107,bool),fun(X7108,bool),hAPP(fun(X7107,X7108),fun(fun(X7107,bool),fun(X7108,bool)),image(X7107,X7108),X7110),hAPP(fun(X7107,bool),fun(X7107,bool),hAPP(fun(X7107,bool),fun(fun(X7107,bool),fun(X7107,bool)),semilattice_inf_inf(fun(X7107,bool)),X7112),hAPP(fun(X7107,bool),fun(X7107,bool),collect(X7107),X7109)))),hAPP(fun(X7107,bool),fun(X7108,bool),hAPP(fun(X7107,X7108),fun(fun(X7107,bool),fun(X7108,bool)),image(X7107,X7108),X7111),hAPP(fun(X7107,bool),fun(X7107,bool),hAPP(fun(X7107,bool),fun(fun(X7107,bool),fun(X7107,bool)),semilattice_inf_inf(fun(X7107,bool)),X7112),hAPP(fun(X7107,bool),fun(X7107,bool),collect(X7107),hAPP(fun(X7107,bool),fun(X7107,bool),hAPP(fun(bool,bool),fun(fun(X7107,bool),fun(X7107,bool)),combb(bool,bool,X7107),fNot),X7109))))),
    inference(variable_rename,[status(thm)],[fact_887_if__image__distrib]) ).

fof(i_0_1547,plain,
    ! [X7503,X7504,X7505,X7506,X7507] :
      ( ( ~ hBOOL(hAPP(fun(X7503,bool),bool,hAPP(X7503,fun(fun(X7503,bool),bool),member(X7503),X7506),X7507))
        | hAPP(fun(X7503,bool),X7504,hAPP(fun(X7503,X7504),fun(fun(X7503,bool),X7504),big_co1399186613setsum(X7503,X7504),hAPP(X7504,fun(X7503,X7504),hAPP(fun(X7503,fun(X7504,X7504)),fun(X7504,fun(X7503,X7504)),combc(X7503,X7504,X7504),hAPP(fun(X7503,X7504),fun(X7503,fun(X7504,X7504)),hAPP(fun(X7503,fun(X7504,fun(X7504,X7504))),fun(fun(X7503,X7504),fun(X7503,fun(X7504,X7504))),combs(X7503,X7504,fun(X7504,X7504)),hAPP(fun(X7503,bool),fun(X7503,fun(X7504,fun(X7504,X7504))),hAPP(fun(bool,fun(X7504,fun(X7504,X7504))),fun(fun(X7503,bool),fun(X7503,fun(X7504,fun(X7504,X7504)))),combb(bool,fun(X7504,fun(X7504,X7504)),X7503),if(X7504)),hAPP(X7503,fun(X7503,bool),fequal(X7503),X7506))),X7505)),zero_zero(X7504))),X7507) = hAPP(X7503,X7504,X7505,X7506)
        | ~ hBOOL(hAPP(fun(X7503,bool),bool,finite_finite_1(X7503),X7507))
        | ~ comm_monoid_add(X7504) )
      & ( hBOOL(hAPP(fun(X7503,bool),bool,hAPP(X7503,fun(fun(X7503,bool),bool),member(X7503),X7506),X7507))
        | hAPP(fun(X7503,bool),X7504,hAPP(fun(X7503,X7504),fun(fun(X7503,bool),X7504),big_co1399186613setsum(X7503,X7504),hAPP(X7504,fun(X7503,X7504),hAPP(fun(X7503,fun(X7504,X7504)),fun(X7504,fun(X7503,X7504)),combc(X7503,X7504,X7504),hAPP(fun(X7503,X7504),fun(X7503,fun(X7504,X7504)),hAPP(fun(X7503,fun(X7504,fun(X7504,X7504))),fun(fun(X7503,X7504),fun(X7503,fun(X7504,X7504))),combs(X7503,X7504,fun(X7504,X7504)),hAPP(fun(X7503,bool),fun(X7503,fun(X7504,fun(X7504,X7504))),hAPP(fun(bool,fun(X7504,fun(X7504,X7504))),fun(fun(X7503,bool),fun(X7503,fun(X7504,fun(X7504,X7504)))),combb(bool,fun(X7504,fun(X7504,X7504)),X7503),if(X7504)),hAPP(X7503,fun(X7503,bool),fequal(X7503),X7506))),X7505)),zero_zero(X7504))),X7507) = zero_zero(X7504)
        | ~ hBOOL(hAPP(fun(X7503,bool),bool,finite_finite_1(X7503),X7507))
        | ~ comm_monoid_add(X7504) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1186])])])]) ).

fof(i_0_1548,plain,
    ! [X4572,X4573,X4574,X4575,X4576,X4577] :
      ( ( hBOOL(hAPP(X4572,bool,hAPP(X4572,fun(X4572,bool),ord_less_eq(X4572),esk47_6(X4572,X4573,X4574,X4575,X4576,X4577)),esk46_6(X4572,X4573,X4574,X4575,X4576,X4577)))
        | hBOOL(hAPP(X4573,bool,hAPP(X4573,fun(X4573,bool),ord_less(X4573),hAPP(X4572,X4573,X4575,X4574)),X4577))
        | ~ hBOOL(hAPP(X4572,bool,hAPP(X4572,fun(X4572,bool),ord_less_eq(X4572),X4574),X4576))
        | ~ hBOOL(hAPP(X4573,bool,hAPP(X4573,fun(X4573,bool),ord_less(X4573),hAPP(X4572,X4573,X4575,X4576)),X4577))
        | ~ order(X4573)
        | ~ order(X4572) )
      & ( ~ hBOOL(hAPP(X4573,bool,hAPP(X4573,fun(X4573,bool),ord_less_eq(X4573),hAPP(X4572,X4573,X4575,esk47_6(X4572,X4573,X4574,X4575,X4576,X4577))),hAPP(X4572,X4573,X4575,esk46_6(X4572,X4573,X4574,X4575,X4576,X4577))))
        | hBOOL(hAPP(X4573,bool,hAPP(X4573,fun(X4573,bool),ord_less(X4573),hAPP(X4572,X4573,X4575,X4574)),X4577))
        | ~ hBOOL(hAPP(X4572,bool,hAPP(X4572,fun(X4572,bool),ord_less_eq(X4572),X4574),X4576))
        | ~ hBOOL(hAPP(X4573,bool,hAPP(X4573,fun(X4573,bool),ord_less(X4573),hAPP(X4572,X4573,X4575,X4576)),X4577))
        | ~ order(X4573)
        | ~ order(X4572) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_xt4])])])])]) ).

fof(i_0_1549,plain,
    ! [X4564,X4565,X4566,X4567,X4568,X4569] :
      ( ( hBOOL(hAPP(X4564,bool,hAPP(X4564,fun(X4564,bool),ord_less(X4564),esk45_6(X4564,X4565,X4566,X4567,X4568,X4569)),esk44_6(X4564,X4565,X4566,X4567,X4568,X4569)))
        | hBOOL(hAPP(X4565,bool,hAPP(X4565,fun(X4565,bool),ord_less(X4565),hAPP(X4564,X4565,X4567,X4566)),X4569))
        | ~ hBOOL(hAPP(X4564,bool,hAPP(X4564,fun(X4564,bool),ord_less(X4564),X4566),X4568))
        | ~ hBOOL(hAPP(X4565,bool,hAPP(X4565,fun(X4565,bool),ord_less_eq(X4565),hAPP(X4564,X4565,X4567,X4568)),X4569))
        | ~ order(X4565)
        | ~ ord(X4564) )
      & ( ~ hBOOL(hAPP(X4565,bool,hAPP(X4565,fun(X4565,bool),ord_less(X4565),hAPP(X4564,X4565,X4567,esk45_6(X4564,X4565,X4566,X4567,X4568,X4569))),hAPP(X4564,X4565,X4567,esk44_6(X4564,X4565,X4566,X4567,X4568,X4569))))
        | hBOOL(hAPP(X4565,bool,hAPP(X4565,fun(X4565,bool),ord_less(X4565),hAPP(X4564,X4565,X4567,X4566)),X4569))
        | ~ hBOOL(hAPP(X4564,bool,hAPP(X4564,fun(X4564,bool),ord_less(X4564),X4566),X4568))
        | ~ hBOOL(hAPP(X4565,bool,hAPP(X4565,fun(X4565,bool),ord_less_eq(X4565),hAPP(X4564,X4565,X4567,X4568)),X4569))
        | ~ order(X4565)
        | ~ ord(X4564) ) ),
    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_xt6])])])])]) ).

fof(i_0_1550,plain,
    ! [X4596,X4597,X4598,X4599,X4600,X4601] :
      ( ( hBOOL(hAPP(X4596,bool,hAPP(X4596,fun(X4596,bool),ord_less_eq(X4596),esk52_6(X4596,X4597,X4598,X4599,X4600,X4601)),esk53_6(X4596,X4597,X4598,X4599,X4600,X4601)))
        | hBOOL(hAPP(X4597,bool,hAPP(X4597,fun(X4597,bool),ord_less(X4597),hAPP(X4596,X4597,X4598,X4600)),X4599))
        | ~ hBOOL(hAPP(X4597,bool,hAPP(X4597,fun(X4597,bool),ord_less(X4597),hAPP(X4596,X4597,X4598,X4601)),X4599))
        | ~ hBOOL(hAPP(X4596,bool,hAPP(X4596,fun(X4596,bool),ord_less_eq(X4596),X4600),X4601))
        | ~ order(X4597)
        | ~ order(X4596) )
      & ( ~ hBOOL(hAPP(X4597,bool,hAPP(X4597,fun(X4597,bool),ord_less_eq(X4597),hAPP(X4596,X4597,X4598,esk52_6(X4596,X4597,X4598,X4599,X4600,X4601))),hAPP(X4596,X4597,X4598,esk53_6(X4596,X4597,X4598,X4599,X4600,X4601))))
        | hBOOL(hAPP(X4597,bool,hAPP(X4597,fun(X4597,bool),ord_less(X4597),hAPP(X4596,X4597,X4598,X4600)),X4599))
        | ~ hBOOL(hAPP(X4597,bool,hAPP(X4597,fun(X4597,bool),ord_less(X4597),hAPP(X4596,X4597,X4598,X4601)),X4599))
        | ~ hBOOL(hAPP(X4596,bool,hAPP(X4596,fun(X4596,bool),ord_less_eq(X4596),X4600),X4601))
        | ~ order(X4597)
        | ~ order(X4596) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_191_order__le__less__subst2])])])])]) ).

fof(i_0_1551,plain,
    ! [X4604,X4605,X4606,X4607,X4608,X4609] :
      ( ( hBOOL(hAPP(X4604,bool,hAPP(X4604,fun(X4604,bool),ord_less(X4604),esk54_6(X4604,X4605,X4606,X4607,X4608,X4609)),esk55_6(X4604,X4605,X4606,X4607,X4608,X4609)))
        | hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less(X4605),hAPP(X4604,X4605,X4606,X4608)),X4607))
        | ~ hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less_eq(X4605),hAPP(X4604,X4605,X4606,X4609)),X4607))
        | ~ hBOOL(hAPP(X4604,bool,hAPP(X4604,fun(X4604,bool),ord_less(X4604),X4608),X4609))
        | ~ order(X4605)
        | ~ order(X4604) )
      & ( ~ hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less(X4605),hAPP(X4604,X4605,X4606,esk54_6(X4604,X4605,X4606,X4607,X4608,X4609))),hAPP(X4604,X4605,X4606,esk55_6(X4604,X4605,X4606,X4607,X4608,X4609))))
        | hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less(X4605),hAPP(X4604,X4605,X4606,X4608)),X4607))
        | ~ hBOOL(hAPP(X4605,bool,hAPP(X4605,fun(X4605,bool),ord_less_eq(X4605),hAPP(X4604,X4605,X4606,X4609)),X4607))
        | ~ hBOOL(hAPP(X4604,bool,hAPP(X4604,fun(X4604,bool),ord_less(X4604),X4608),X4609))
        | ~ order(X4605)
        | ~ order(X4604) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_192_order__less__le__subst2])])])])]) ).

fof(i_0_1552,plain,
    ! [X4444,X4445,X4446,X4447,X4448,X4449] :
      ( ( hBOOL(hAPP(X4445,bool,hAPP(X4445,fun(X4445,bool),ord_less_eq(X4445),esk42_6(X4444,X4445,X4446,X4447,X4448,X4449)),esk41_6(X4444,X4445,X4446,X4447,X4448,X4449)))
        | hBOOL(hAPP(X4444,bool,hAPP(X4444,fun(X4444,bool),ord_less(X4444),X4446),hAPP(X4445,X4444,X4447,X4449)))
        | ~ hBOOL(hAPP(X4444,bool,hAPP(X4444,fun(X4444,bool),ord_less(X4444),X4446),hAPP(X4445,X4444,X4447,X4448)))
        | ~ hBOOL(hAPP(X4445,bool,hAPP(X4445,fun(X4445,bool),ord_less_eq(X4445),X4448),X4449))
        | ~ order(X4445)
        | ~ order(X4444) )
      & ( ~ hBOOL(hAPP(X4444,bool,hAPP(X4444,fun(X4444,bool),ord_less_eq(X4444),hAPP(X4445,X4444,X4447,esk42_6(X4444,X4445,X4446,X4447,X4448,X4449))),hAPP(X4445,X4444,X4447,esk41_6(X4444,X4445,X4446,X4447,X4448,X4449))))
        | hBOOL(hAPP(X4444,bool,hAPP(X4444,fun(X4444,bool),ord_less(X4444),X4446),hAPP(X4445,X4444,X4447,X4449)))
        | ~ hBOOL(hAPP(X4444,bool,hAPP(X4444,fun(X4444,bool),ord_less(X4444),X4446),hAPP(X4445,X4444,X4447,X4448)))
        | ~ hBOOL(hAPP(X4445,bool,hAPP(X4445,fun(X4445,bool),ord_less_eq(X4445),X4448),X4449))
        | ~ order(X4445)
        | ~ order(X4444) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_xt7])])])])]) ).

fof(i_0_1553,plain,
    ! [X4436,X4437,X4438,X4439,X4440,X4441] :
      ( ( hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less(X4437),esk40_6(X4436,X4437,X4438,X4439,X4440,X4441)),esk39_6(X4436,X4437,X4438,X4439,X4440,X4441)))
        | hBOOL(hAPP(X4436,bool,hAPP(X4436,fun(X4436,bool),ord_less(X4436),X4438),hAPP(X4437,X4436,X4439,X4441)))
        | ~ hBOOL(hAPP(X4436,bool,hAPP(X4436,fun(X4436,bool),ord_less_eq(X4436),X4438),hAPP(X4437,X4436,X4439,X4440)))
        | ~ hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less(X4437),X4440),X4441))
        | ~ order(X4437)
        | ~ order(X4436) )
      & ( ~ hBOOL(hAPP(X4436,bool,hAPP(X4436,fun(X4436,bool),ord_less(X4436),hAPP(X4437,X4436,X4439,esk40_6(X4436,X4437,X4438,X4439,X4440,X4441))),hAPP(X4437,X4436,X4439,esk39_6(X4436,X4437,X4438,X4439,X4440,X4441))))
        | hBOOL(hAPP(X4436,bool,hAPP(X4436,fun(X4436,bool),ord_less(X4436),X4438),hAPP(X4437,X4436,X4439,X4441)))
        | ~ hBOOL(hAPP(X4436,bool,hAPP(X4436,fun(X4436,bool),ord_less_eq(X4436),X4438),hAPP(X4437,X4436,X4439,X4440)))
        | ~ hBOOL(hAPP(X4437,bool,hAPP(X4437,fun(X4437,bool),ord_less(X4437),X4440),X4441))
        | ~ order(X4437)
        | ~ order(X4436) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_xt5])])])])]) ).

fof(i_0_1554,plain,
    ! [X4588,X4589,X4590,X4591,X4592,X4593] :
      ( ( hBOOL(hAPP(X4589,bool,hAPP(X4589,fun(X4589,bool),ord_less_eq(X4589),esk50_6(X4588,X4589,X4590,X4591,X4592,X4593)),esk51_6(X4588,X4589,X4590,X4591,X4592,X4593)))
        | hBOOL(hAPP(X4588,bool,hAPP(X4588,fun(X4588,bool),ord_less(X4588),X4591),hAPP(X4589,X4588,X4592,X4590)))
        | ~ hBOOL(hAPP(X4589,bool,hAPP(X4589,fun(X4589,bool),ord_less_eq(X4589),X4593),X4590))
        | ~ hBOOL(hAPP(X4588,bool,hAPP(X4588,fun(X4588,bool),ord_less(X4588),X4591),hAPP(X4589,X4588,X4592,X4593)))
        | ~ order(X4589)
        | ~ order(X4588) )
      & ( ~ hBOOL(hAPP(X4588,bool,hAPP(X4588,fun(X4588,bool),ord_less_eq(X4588),hAPP(X4589,X4588,X4592,esk50_6(X4588,X4589,X4590,X4591,X4592,X4593))),hAPP(X4589,X4588,X4592,esk51_6(X4588,X4589,X4590,X4591,X4592,X4593))))
        | hBOOL(hAPP(X4588,bool,hAPP(X4588,fun(X4588,bool),ord_less(X4588),X4591),hAPP(X4589,X4588,X4592,X4590)))
        | ~ hBOOL(hAPP(X4589,bool,hAPP(X4589,fun(X4589,bool),ord_less_eq(X4589),X4593),X4590))
        | ~ hBOOL(hAPP(X4588,bool,hAPP(X4588,fun(X4588,bool),ord_less(X4588),X4591),hAPP(X4589,X4588,X4592,X4593)))
        | ~ order(X4589)
        | ~ order(X4588) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_190_order__less__le__subst1])])])])]) ).

fof(i_0_1555,plain,
    ! [X4580,X4581,X4582,X4583,X4584,X4585] :
      ( ( hBOOL(hAPP(X4581,bool,hAPP(X4581,fun(X4581,bool),ord_less(X4581),esk48_6(X4580,X4581,X4582,X4583,X4584,X4585)),esk49_6(X4580,X4581,X4582,X4583,X4584,X4585)))
        | hBOOL(hAPP(X4580,bool,hAPP(X4580,fun(X4580,bool),ord_less(X4580),X4583),hAPP(X4581,X4580,X4584,X4582)))
        | ~ hBOOL(hAPP(X4581,bool,hAPP(X4581,fun(X4581,bool),ord_less(X4581),X4585),X4582))
        | ~ hBOOL(hAPP(X4580,bool,hAPP(X4580,fun(X4580,bool),ord_less_eq(X4580),X4583),hAPP(X4581,X4580,X4584,X4585)))
        | ~ order(X4581)
        | ~ order(X4580) )
      & ( ~ hBOOL(hAPP(X4580,bool,hAPP(X4580,fun(X4580,bool),ord_less(X4580),hAPP(X4581,X4580,X4584,esk48_6(X4580,X4581,X4582,X4583,X4584,X4585))),hAPP(X4581,X4580,X4584,esk49_6(X4580,X4581,X4582,X4583,X4584,X4585))))
        | hBOOL(hAPP(X4580,bool,hAPP(X4580,fun(X4580,bool),ord_less(X4580),X4583),hAPP(X4581,X4580,X4584,X4582)))
        | ~ hBOOL(hAPP(X4581,bool,hAPP(X4581,fun(X4581,bool),ord_less(X4581),X4585),X4582))
        | ~ hBOOL(hAPP(X4580,bool,hAPP(X4580,fun(X4580,bool),ord_less_eq(X4580),X4583),hAPP(X4581,X4580,X4584,X4585)))
        | ~ order(X4581)
        | ~ order(X4580) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_order__le__less__subst1])])])])]) ).

cnf(i_0_1556,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1187]) ).

cnf(i_0_1557,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1187]) ).

cnf(i_0_1558,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X6)
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X6)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1188]) ).

cnf(i_0_1559,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1189]) ).

cnf(i_0_1560,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1189]) ).

cnf(i_0_1561,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X1)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1187]) ).

cnf(i_0_1562,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1187]) ).

cnf(i_0_1563,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X6)
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X6)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1188]) ).

cnf(i_0_1564,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1189]) ).

cnf(i_0_1565,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1189]) ).

fof(i_0_1566,plain,
    ! [X5236,X5237] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X5237))
      | 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)),X5237))),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,X5236))))) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_card__less])]) ).

fof(i_0_1567,plain,
    ! [X4156] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),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_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),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_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),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_1998540521e_indi,nat,h,X4156)),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_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),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_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X4156) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X4156)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X4156)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1190])])]) ).

fof(i_0_1568,plain,
    ! [X6269,X6270,X6271,X6272,X6273] :
      ( ~ comm_monoid_mult(X6270)
      | ~ hBOOL(hAPP(fun(X6269,bool),bool,finite_finite_1(X6269),X6273))
      | hAPP(fun(X6269,bool),X6270,hAPP(X6270,fun(fun(X6269,bool),X6270),hAPP(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270)),hAPP(fun(X6270,fun(X6270,X6270)),fun(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270))),finite_fold_image(X6270,X6269),times_times(X6270)),hAPP(fun(X6269,X6270),fun(X6269,X6270),hAPP(fun(X6269,fun(X6270,X6270)),fun(fun(X6269,X6270),fun(X6269,X6270)),combs(X6269,X6270,X6270),hAPP(fun(X6269,X6270),fun(X6269,fun(X6270,X6270)),hAPP(fun(X6270,fun(X6270,X6270)),fun(fun(X6269,X6270),fun(X6269,fun(X6270,X6270))),combb(X6270,fun(X6270,X6270),X6269),times_times(X6270)),X6271)),X6272)),one_one(X6270)),X6273) = hAPP(X6270,X6270,hAPP(X6270,fun(X6270,X6270),times_times(X6270),hAPP(fun(X6269,bool),X6270,hAPP(X6270,fun(fun(X6269,bool),X6270),hAPP(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270)),hAPP(fun(X6270,fun(X6270,X6270)),fun(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270))),finite_fold_image(X6270,X6269),times_times(X6270)),X6271),one_one(X6270)),X6273)),hAPP(fun(X6269,bool),X6270,hAPP(X6270,fun(fun(X6269,bool),X6270),hAPP(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270)),hAPP(fun(X6270,fun(X6270,X6270)),fun(fun(X6269,X6270),fun(X6270,fun(fun(X6269,bool),X6270))),finite_fold_image(X6270,X6269),times_times(X6270)),X6272),one_one(X6270)),X6273)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_697_fold__image__distrib])])]) ).

fof(i_0_1569,plain,
    ! [X7459,X7460,X7461,X7462,X7463,X7464] :
      ( ~ comm_monoid_add(X7461)
      | hAPP(fun(X7459,bool),X7461,hAPP(fun(X7459,X7461),fun(fun(X7459,bool),X7461),big_co1399186613setsum(X7459,X7461),hAPP(fun(X7460,bool),fun(X7459,X7461),hAPP(fun(X7459,fun(fun(X7460,bool),X7461)),fun(fun(X7460,bool),fun(X7459,X7461)),combc(X7459,fun(X7460,bool),X7461),hAPP(fun(X7459,fun(X7460,X7461)),fun(X7459,fun(fun(X7460,bool),X7461)),hAPP(fun(fun(X7460,X7461),fun(fun(X7460,bool),X7461)),fun(fun(X7459,fun(X7460,X7461)),fun(X7459,fun(fun(X7460,bool),X7461))),combb(fun(X7460,X7461),fun(fun(X7460,bool),X7461),X7459),big_co1399186613setsum(X7460,X7461)),X7462)),X7463)),X7464) = hAPP(fun(X7460,bool),X7461,hAPP(fun(X7460,X7461),fun(fun(X7460,bool),X7461),big_co1399186613setsum(X7460,X7461),hAPP(fun(X7459,bool),fun(X7460,X7461),hAPP(fun(X7460,fun(fun(X7459,bool),X7461)),fun(fun(X7459,bool),fun(X7460,X7461)),combc(X7460,fun(X7459,bool),X7461),hAPP(fun(X7460,fun(X7459,X7461)),fun(X7460,fun(fun(X7459,bool),X7461)),hAPP(fun(fun(X7459,X7461),fun(fun(X7459,bool),X7461)),fun(fun(X7460,fun(X7459,X7461)),fun(X7460,fun(fun(X7459,bool),X7461))),combb(fun(X7459,X7461),fun(fun(X7459,bool),X7461),X7460),big_co1399186613setsum(X7459,X7461)),hAPP(fun(X7459,fun(X7460,X7461)),fun(X7460,fun(X7459,X7461)),combc(X7459,X7460,X7461),X7462))),X7464)),X7463) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_978_setsum__commute])])]) ).

fof(i_0_1570,plain,
    ! [X3957] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) != n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) = n
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X3957) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X3957) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X3957)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) != n
        | hAPP(arrow_1998540521e_indi,nat,h,X3957) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hAPP(arrow_1998540521e_indi,nat,h,X3957) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( hAPP(arrow_1998540521e_indi,nat,h,X3957) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X3957))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1191])])]) ).

fof(i_0_1571,plain,
    ! [X7024,X7025,X7026,X7027,X7028] :
      ( ~ comm_monoid_mult(X7025)
      | ~ hBOOL(hAPP(fun(X7024,bool),bool,finite_finite_1(X7024),X7028))
      | ~ hBOOL(hAPP(fun(X7024,bool),bool,finite_finite_1(X7024),X7027))
      | hAPP(X7025,X7025,hAPP(X7025,fun(X7025,X7025),times_times(X7025),hAPP(fun(X7024,bool),X7025,hAPP(X7025,fun(fun(X7024,bool),X7025),hAPP(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025)),hAPP(fun(X7025,fun(X7025,X7025)),fun(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025))),finite_fold_image(X7025,X7024),times_times(X7025)),X7026),one_one(X7025)),X7028)),hAPP(fun(X7024,bool),X7025,hAPP(X7025,fun(fun(X7024,bool),X7025),hAPP(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025)),hAPP(fun(X7025,fun(X7025,X7025)),fun(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025))),finite_fold_image(X7025,X7024),times_times(X7025)),X7026),one_one(X7025)),X7027)) = hAPP(X7025,X7025,hAPP(X7025,fun(X7025,X7025),times_times(X7025),hAPP(fun(X7024,bool),X7025,hAPP(X7025,fun(fun(X7024,bool),X7025),hAPP(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025)),hAPP(fun(X7025,fun(X7025,X7025)),fun(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025))),finite_fold_image(X7025,X7024),times_times(X7025)),X7026),one_one(X7025)),hAPP(fun(X7024,bool),fun(X7024,bool),hAPP(fun(X7024,bool),fun(fun(X7024,bool),fun(X7024,bool)),semilattice_sup_sup(fun(X7024,bool)),X7028),X7027))),hAPP(fun(X7024,bool),X7025,hAPP(X7025,fun(fun(X7024,bool),X7025),hAPP(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025)),hAPP(fun(X7025,fun(X7025,X7025)),fun(fun(X7024,X7025),fun(X7025,fun(fun(X7024,bool),X7025))),finite_fold_image(X7025,X7024),times_times(X7025)),X7026),one_one(X7025)),hAPP(fun(X7024,bool),fun(X7024,bool),hAPP(fun(X7024,bool),fun(fun(X7024,bool),fun(X7024,bool)),semilattice_inf_inf(fun(X7024,bool)),X7028),X7027))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_866_fold__image__Un__Int])])]) ).

fof(i_0_1572,plain,
    ! [X3982,X3983,X3984,X3985,X3986,X3988,X3993,X3994] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3983)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3984)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3983,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3984,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3984),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3983),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3982)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3984)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3983)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3983,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3984,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3984),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3983),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3982)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3983)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3984)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3983,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3984,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3984),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3983),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3982)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3984)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3982,X3983)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3983,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3985),X3986)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3984,esk9_5(X3982,X3983,X3984,X3985,X3986))))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3984),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3983),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3982)) )
      & ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk10_1(X3988)),arrow_301600364e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) )
      & ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk11_1(X3988)),arrow_301600364e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X3988),X3993)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X3988),X3993)))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X3988),X3994)))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X3988),X3994)))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3988,esk10_1(X3988))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3988,esk11_1(X3988))))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3988,esk10_1(X3988))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X3988)),esk13_1(X3988))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3988,esk11_1(X3988))))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3988)) ) ),
    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_1573,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1192]) ).

cnf(i_0_1574,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1192]) ).

cnf(i_0_1575,plain,
    ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X2),X1))
    | ti(arrow_2142409994le_alt,esk25_2(X1,X2)) != ti(arrow_2142409994le_alt,esk26_2(X1,X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1193]) ).

fof(i_0_1576,plain,
    ! [X4913,X4914,X4915] :
      ( ( hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),X4914)))
        | ~ hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),hAPP(fun(X4913,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,bool)),combs(X4913,bool,bool),hAPP(fun(X4913,bool),fun(X4913,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,fun(bool,bool))),combb(bool,fun(bool,bool),X4913),fdisj),X4914)),X4915)))) )
      & ( hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),X4915)))
        | ~ hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),hAPP(fun(X4913,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,bool)),combs(X4913,bool,bool),hAPP(fun(X4913,bool),fun(X4913,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,fun(bool,bool))),combb(bool,fun(bool,bool),X4913),fdisj),X4914)),X4915)))) )
      & ( ~ hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),X4914)))
        | ~ hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),X4915)))
        | hBOOL(hAPP(fun(X4913,bool),bool,finite_finite_1(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),collect(X4913),hAPP(fun(X4913,bool),fun(X4913,bool),hAPP(fun(X4913,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,bool)),combs(X4913,bool,bool),hAPP(fun(X4913,bool),fun(X4913,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4913,bool),fun(X4913,fun(bool,bool))),combb(bool,fun(bool,bool),X4913),fdisj),X4914)),X4915)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_finite__Collect__disjI])])]) ).

cnf(i_0_1577,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

cnf(i_0_1578,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1192]) ).

cnf(i_0_1579,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1192]) ).

cnf(i_0_1580,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1195]) ).

cnf(i_0_1581,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1195]) ).

fof(i_0_1582,plain,
    ! [X5821,X5822,X5823,X5824,X5825,X5826,X5827,X5828,X5829,X5830,X5831] :
      ( ~ hBOOL(hAPP(fun(fun(X5823,X5824),bool),bool,hAPP(fun(X5823,X5824),fun(fun(fun(X5823,X5824),bool),bool),member(fun(X5823,X5824)),X5829),hAPP(fun(X5823,fun(X5824,bool)),fun(fun(X5823,X5824),bool),hAPP(fun(X5823,bool),fun(fun(X5823,fun(X5824,bool)),fun(fun(X5823,X5824),bool)),pi(X5823,X5824),X5830),hAPP(fun(X5824,bool),fun(X5823,fun(X5824,bool)),combk(fun(X5824,bool),X5823),X5831))))
      | ~ hBOOL(hAPP(fun(fun(X5824,X5822),bool),bool,hAPP(fun(X5824,X5822),fun(fun(fun(X5824,X5822),bool),bool),member(fun(X5824,X5822)),X5827),hAPP(fun(X5824,fun(X5822,bool)),fun(fun(X5824,X5822),bool),hAPP(fun(X5824,bool),fun(fun(X5824,fun(X5822,bool)),fun(fun(X5824,X5822),bool)),pi(X5824,X5822),X5831),hAPP(fun(X5822,bool),fun(X5824,fun(X5822,bool)),combk(fun(X5822,bool),X5824),X5828))))
      | ~ hBOOL(hAPP(fun(fun(X5822,X5821),bool),bool,hAPP(fun(X5822,X5821),fun(fun(fun(X5822,X5821),bool),bool),member(fun(X5822,X5821)),X5825),hAPP(fun(X5822,fun(X5821,bool)),fun(fun(X5822,X5821),bool),hAPP(fun(X5822,bool),fun(fun(X5822,fun(X5821,bool)),fun(fun(X5822,X5821),bool)),pi(X5822,X5821),X5828),hAPP(fun(X5821,bool),fun(X5822,fun(X5821,bool)),combk(fun(X5821,bool),X5822),X5826))))
      | hAPP(fun(X5823,X5822),fun(X5823,X5821),hAPP(fun(X5822,X5821),fun(fun(X5823,X5822),fun(X5823,X5821)),hAPP(fun(X5823,bool),fun(fun(X5822,X5821),fun(fun(X5823,X5822),fun(X5823,X5821))),compose(X5823,X5822,X5821),X5830),X5825),hAPP(fun(X5823,X5824),fun(X5823,X5822),hAPP(fun(X5824,X5822),fun(fun(X5823,X5824),fun(X5823,X5822)),hAPP(fun(X5823,bool),fun(fun(X5824,X5822),fun(fun(X5823,X5824),fun(X5823,X5822))),compose(X5823,X5824,X5822),X5830),X5827),X5829)) = hAPP(fun(X5823,X5824),fun(X5823,X5821),hAPP(fun(X5824,X5821),fun(fun(X5823,X5824),fun(X5823,X5821)),hAPP(fun(X5823,bool),fun(fun(X5824,X5821),fun(fun(X5823,X5824),fun(X5823,X5821))),compose(X5823,X5824,X5821),X5830),hAPP(fun(X5824,X5822),fun(X5824,X5821),hAPP(fun(X5822,X5821),fun(fun(X5824,X5822),fun(X5824,X5821)),hAPP(fun(X5824,bool),fun(fun(X5822,X5821),fun(fun(X5824,X5822),fun(X5824,X5821))),compose(X5824,X5822,X5821),X5831),X5825),X5827)),X5829) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_565_compose__assoc])]) ).

fof(i_0_1583,plain,
    ! [X5832,X5833,X5834,X5835,X5836,X5837,X5838,X5839] :
      ( ~ hBOOL(hAPP(fun(fun(X5833,X5834),bool),bool,hAPP(fun(X5833,X5834),fun(fun(fun(X5833,X5834),bool),bool),member(fun(X5833,X5834)),X5837),hAPP(fun(X5833,fun(X5834,bool)),fun(fun(X5833,X5834),bool),hAPP(fun(X5833,bool),fun(fun(X5833,fun(X5834,bool)),fun(fun(X5833,X5834),bool)),pi(X5833,X5834),X5838),hAPP(fun(X5834,bool),fun(X5833,fun(X5834,bool)),combk(fun(X5834,bool),X5833),X5839))))
      | ~ hBOOL(hAPP(fun(fun(X5834,X5832),bool),bool,hAPP(fun(X5834,X5832),fun(fun(fun(X5834,X5832),bool),bool),member(fun(X5834,X5832)),X5835),hAPP(fun(X5834,fun(X5832,bool)),fun(fun(X5834,X5832),bool),hAPP(fun(X5834,bool),fun(fun(X5834,fun(X5832,bool)),fun(fun(X5834,X5832),bool)),pi(X5834,X5832),X5839),hAPP(fun(X5832,bool),fun(X5834,fun(X5832,bool)),combk(fun(X5832,bool),X5834),X5836))))
      | hBOOL(hAPP(fun(fun(X5833,X5832),bool),bool,hAPP(fun(X5833,X5832),fun(fun(fun(X5833,X5832),bool),bool),member(fun(X5833,X5832)),hAPP(fun(X5833,X5834),fun(X5833,X5832),hAPP(fun(X5834,X5832),fun(fun(X5833,X5834),fun(X5833,X5832)),hAPP(fun(X5833,bool),fun(fun(X5834,X5832),fun(fun(X5833,X5834),fun(X5833,X5832))),compose(X5833,X5834,X5832),X5838),X5835),X5837)),hAPP(fun(X5833,fun(X5832,bool)),fun(fun(X5833,X5832),bool),hAPP(fun(X5833,bool),fun(fun(X5833,fun(X5832,bool)),fun(fun(X5833,X5832),bool)),pi(X5833,X5832),X5838),hAPP(fun(X5832,bool),fun(X5833,fun(X5832,bool)),combk(fun(X5832,bool),X5833),X5836)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_566_funcset__compose])]) ).

fof(i_0_1584,plain,
    ! [X7411,X7412,X7413,X7414,X7415] :
      ( ( hBOOL(hAPP(fun(X7411,bool),bool,hAPP(X7411,fun(fun(X7411,bool),bool),member(X7411),esk173_5(X7411,X7412,X7413,X7414,X7415)),hAPP(fun(X7411,bool),fun(X7411,bool),hAPP(fun(X7411,bool),fun(fun(X7411,bool),fun(X7411,bool)),semilattice_inf_inf(fun(X7411,bool)),X7415),X7414)))
        | hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),hAPP(fun(X7411,bool),fun(X7411,bool),hAPP(fun(X7411,bool),fun(fun(X7411,bool),fun(X7411,bool)),semilattice_sup_sup(fun(X7411,bool)),X7415),X7414)) = hAPP(X7412,X7412,hAPP(X7412,fun(X7412,X7412),times_times(X7412),hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),X7415)),hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),X7414))
        | ~ hBOOL(hAPP(fun(X7411,bool),bool,finite_finite_1(X7411),X7414))
        | ~ hBOOL(hAPP(fun(X7411,bool),bool,finite_finite_1(X7411),X7415))
        | ~ comm_monoid_mult(X7412) )
      & ( hAPP(X7411,X7412,X7413,esk173_5(X7411,X7412,X7413,X7414,X7415)) != one_one(X7412)
        | hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),hAPP(fun(X7411,bool),fun(X7411,bool),hAPP(fun(X7411,bool),fun(fun(X7411,bool),fun(X7411,bool)),semilattice_sup_sup(fun(X7411,bool)),X7415),X7414)) = hAPP(X7412,X7412,hAPP(X7412,fun(X7412,X7412),times_times(X7412),hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),X7415)),hAPP(fun(X7411,bool),X7412,hAPP(X7412,fun(fun(X7411,bool),X7412),hAPP(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412)),hAPP(fun(X7412,fun(X7412,X7412)),fun(fun(X7411,X7412),fun(X7412,fun(fun(X7411,bool),X7412))),finite_fold_image(X7412,X7411),times_times(X7412)),X7413),one_one(X7412)),X7414))
        | ~ hBOOL(hAPP(fun(X7411,bool),bool,finite_finite_1(X7411),X7414))
        | ~ hBOOL(hAPP(fun(X7411,bool),bool,finite_finite_1(X7411),X7415))
        | ~ comm_monoid_mult(X7412) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_968_fold__image__Un__one])])])])]) ).

fof(i_0_1585,plain,
    ! [X4935,X4936] : 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),X4935)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X4936))))),
    inference(variable_rename,[status(thm)],[fact_301_finite__M__bounded__by__nat]) ).

fof(i_0_1586,plain,
    ! [X6487,X6488,X6489,X6490,X6491,X6492,X6493] :
      ( ~ hBOOL(hAPP(fun(X6487,bool),bool,hAPP(fun(X6487,X6488),fun(fun(X6487,bool),bool),inj_on(X6487,X6488),X6491),hAPP(fun(X6489,bool),fun(X6487,bool),hAPP(fun(X6489,X6487),fun(fun(X6489,bool),fun(X6487,bool)),image(X6489,X6487),X6492),X6493)))
      | ~ hBOOL(hAPP(fun(X6489,bool),bool,hAPP(fun(X6489,X6487),fun(fun(X6489,bool),bool),inj_on(X6489,X6487),X6492),X6493))
      | ~ hBOOL(hAPP(fun(X6488,bool),bool,hAPP(X6488,fun(fun(X6488,bool),bool),member(X6488),X6490),hAPP(fun(X6487,bool),fun(X6488,bool),hAPP(fun(X6487,X6488),fun(fun(X6487,bool),fun(X6488,bool)),image(X6487,X6488),X6491),hAPP(fun(X6489,bool),fun(X6487,bool),hAPP(fun(X6489,X6487),fun(fun(X6489,bool),fun(X6487,bool)),image(X6489,X6487),X6492),X6493))))
      | hAPP(X6488,X6489,hAPP(fun(X6489,X6488),fun(X6488,X6489),hAPP(fun(X6489,bool),fun(fun(X6489,X6488),fun(X6488,X6489)),hilbert_inv_into(X6489,X6488),X6493),hAPP(fun(X6489,X6487),fun(X6489,X6488),hAPP(fun(X6487,X6488),fun(fun(X6489,X6487),fun(X6489,X6488)),comp(X6487,X6488,X6489),X6491),X6492)),X6490) = hAPP(X6488,X6489,hAPP(fun(X6488,X6487),fun(X6488,X6489),hAPP(fun(X6487,X6489),fun(fun(X6488,X6487),fun(X6488,X6489)),comp(X6487,X6489,X6488),hAPP(fun(X6489,X6487),fun(X6487,X6489),hAPP(fun(X6489,bool),fun(fun(X6489,X6487),fun(X6487,X6489)),hilbert_inv_into(X6489,X6487),X6493),X6492)),hAPP(fun(X6487,X6488),fun(X6488,X6487),hAPP(fun(X6487,bool),fun(fun(X6487,X6488),fun(X6488,X6487)),hilbert_inv_into(X6487,X6488),hAPP(fun(X6489,bool),fun(X6487,bool),hAPP(fun(X6489,X6487),fun(fun(X6489,bool),fun(X6487,bool)),image(X6489,X6487),X6492),X6493)),X6491)),X6490) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_737_inv__into__comp])]) ).

fof(i_0_1587,plain,
    ! [X6494,X6495,X6496,X6497,X6498,X6499,X6500] :
      ( ~ hBOOL(hAPP(fun(X6494,bool),bool,hAPP(fun(X6494,X6495),fun(fun(X6494,bool),bool),inj_on(X6494,X6495),X6498),hAPP(fun(X6496,bool),fun(X6494,bool),hAPP(fun(X6496,X6494),fun(fun(X6496,bool),fun(X6494,bool)),image(X6496,X6494),X6499),X6500)))
      | ~ hBOOL(hAPP(fun(X6496,bool),bool,hAPP(fun(X6496,X6494),fun(fun(X6496,bool),bool),inj_on(X6496,X6494),X6499),X6500))
      | ~ hBOOL(hAPP(fun(X6495,bool),bool,hAPP(X6495,fun(fun(X6495,bool),bool),member(X6495),X6497),hAPP(fun(X6494,bool),fun(X6495,bool),hAPP(fun(X6494,X6495),fun(fun(X6494,bool),fun(X6495,bool)),image(X6494,X6495),X6498),hAPP(fun(X6496,bool),fun(X6494,bool),hAPP(fun(X6496,X6494),fun(fun(X6496,bool),fun(X6494,bool)),image(X6496,X6494),X6499),X6500))))
      | hAPP(X6495,X6496,hAPP(fun(X6496,X6495),fun(X6495,X6496),hAPP(fun(X6496,bool),fun(fun(X6496,X6495),fun(X6495,X6496)),the_inv_into(X6496,X6495),X6500),hAPP(fun(X6496,X6494),fun(X6496,X6495),hAPP(fun(X6494,X6495),fun(fun(X6496,X6494),fun(X6496,X6495)),comp(X6494,X6495,X6496),X6498),X6499)),X6497) = hAPP(X6495,X6496,hAPP(fun(X6495,X6494),fun(X6495,X6496),hAPP(fun(X6494,X6496),fun(fun(X6495,X6494),fun(X6495,X6496)),comp(X6494,X6496,X6495),hAPP(fun(X6496,X6494),fun(X6494,X6496),hAPP(fun(X6496,bool),fun(fun(X6496,X6494),fun(X6494,X6496)),the_inv_into(X6496,X6494),X6500),X6499)),hAPP(fun(X6494,X6495),fun(X6495,X6494),hAPP(fun(X6494,bool),fun(fun(X6494,X6495),fun(X6495,X6494)),the_inv_into(X6494,X6495),hAPP(fun(X6496,bool),fun(X6494,bool),hAPP(fun(X6496,X6494),fun(fun(X6496,bool),fun(X6494,bool)),image(X6496,X6494),X6499),X6500)),X6498)),X6497) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_738_the__inv__into__comp])]) ).

cnf(i_0_1588,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1589,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

fof(i_0_1590,plain,
    ! [X6803,X6804,X6805,X6806] :
      ( ( ~ hBOOL(hAPP(X6803,bool,hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,bool),fun(fun(X6803,bool),fun(X6803,bool)),semilattice_sup_sup(fun(X6803,bool)),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,fun(fun(X6803,bool),bool)),fun(fun(X6803,bool),fun(X6803,bool)),combc(X6803,fun(X6803,bool),bool),member(X6803)),X6804)),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,fun(fun(X6803,bool),bool)),fun(fun(X6803,bool),fun(X6803,bool)),combc(X6803,fun(X6803,bool),bool),member(X6803)),X6805)),X6806))
        | hBOOL(hAPP(fun(X6803,bool),bool,hAPP(X6803,fun(fun(X6803,bool),bool),member(X6803),X6806),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,bool),fun(fun(X6803,bool),fun(X6803,bool)),semilattice_sup_sup(fun(X6803,bool)),X6804),X6805))) )
      & ( ~ hBOOL(hAPP(fun(X6803,bool),bool,hAPP(X6803,fun(fun(X6803,bool),bool),member(X6803),X6806),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,bool),fun(fun(X6803,bool),fun(X6803,bool)),semilattice_sup_sup(fun(X6803,bool)),X6804),X6805)))
        | hBOOL(hAPP(X6803,bool,hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,bool),fun(fun(X6803,bool),fun(X6803,bool)),semilattice_sup_sup(fun(X6803,bool)),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,fun(fun(X6803,bool),bool)),fun(fun(X6803,bool),fun(X6803,bool)),combc(X6803,fun(X6803,bool),bool),member(X6803)),X6804)),hAPP(fun(X6803,bool),fun(X6803,bool),hAPP(fun(X6803,fun(fun(X6803,bool),bool)),fun(fun(X6803,bool),fun(X6803,bool)),combc(X6803,fun(X6803,bool),bool),member(X6803)),X6805)),X6806)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_804_sup__Un__eq])]) ).

fof(i_0_1591,plain,
    ! [X7151,X7152,X7153,X7154] :
      ( ( ~ hBOOL(hAPP(X7151,bool,hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,bool),fun(fun(X7151,bool),fun(X7151,bool)),semilattice_inf_inf(fun(X7151,bool)),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,fun(fun(X7151,bool),bool)),fun(fun(X7151,bool),fun(X7151,bool)),combc(X7151,fun(X7151,bool),bool),member(X7151)),X7152)),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,fun(fun(X7151,bool),bool)),fun(fun(X7151,bool),fun(X7151,bool)),combc(X7151,fun(X7151,bool),bool),member(X7151)),X7153)),X7154))
        | hBOOL(hAPP(fun(X7151,bool),bool,hAPP(X7151,fun(fun(X7151,bool),bool),member(X7151),X7154),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,bool),fun(fun(X7151,bool),fun(X7151,bool)),semilattice_inf_inf(fun(X7151,bool)),X7152),X7153))) )
      & ( ~ hBOOL(hAPP(fun(X7151,bool),bool,hAPP(X7151,fun(fun(X7151,bool),bool),member(X7151),X7154),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,bool),fun(fun(X7151,bool),fun(X7151,bool)),semilattice_inf_inf(fun(X7151,bool)),X7152),X7153)))
        | hBOOL(hAPP(X7151,bool,hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,bool),fun(fun(X7151,bool),fun(X7151,bool)),semilattice_inf_inf(fun(X7151,bool)),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,fun(fun(X7151,bool),bool)),fun(fun(X7151,bool),fun(X7151,bool)),combc(X7151,fun(X7151,bool),bool),member(X7151)),X7152)),hAPP(fun(X7151,bool),fun(X7151,bool),hAPP(fun(X7151,fun(fun(X7151,bool),bool)),fun(fun(X7151,bool),fun(X7151,bool)),combc(X7151,fun(X7151,bool),bool),member(X7151)),X7153)),X7154)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_897_inf__Int__eq])]) ).

cnf(i_0_1592,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1195]) ).

cnf(i_0_1593,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1195]) ).

fof(i_0_1594,plain,
    ! [X4806,X4807,X4808,X4809,X4810] :
      ( ( hBOOL(hAPP(fun(X4807,bool),bool,hAPP(X4807,fun(fun(X4807,bool),bool),member(X4807),esk59_5(X4806,X4807,X4808,X4809,X4810)),X4810))
        | hBOOL(hAPP(fun(fun(X4807,X4806),bool),bool,hAPP(fun(fun(X4807,X4806),bool),fun(fun(fun(X4807,X4806),bool),bool),ord_less_eq(fun(fun(X4807,X4806),bool)),hAPP(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool),hAPP(fun(X4807,bool),fun(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool)),pi(X4807,X4806),X4810),X4808)),hAPP(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool),hAPP(fun(X4807,bool),fun(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool)),pi(X4807,X4806),X4810),X4809))) )
      & ( ~ hBOOL(hAPP(fun(X4806,bool),bool,hAPP(fun(X4806,bool),fun(fun(X4806,bool),bool),ord_less_eq(fun(X4806,bool)),hAPP(X4807,fun(X4806,bool),X4808,esk59_5(X4806,X4807,X4808,X4809,X4810))),hAPP(X4807,fun(X4806,bool),X4809,esk59_5(X4806,X4807,X4808,X4809,X4810))))
        | hBOOL(hAPP(fun(fun(X4807,X4806),bool),bool,hAPP(fun(fun(X4807,X4806),bool),fun(fun(fun(X4807,X4806),bool),bool),ord_less_eq(fun(fun(X4807,X4806),bool)),hAPP(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool),hAPP(fun(X4807,bool),fun(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool)),pi(X4807,X4806),X4810),X4808)),hAPP(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool),hAPP(fun(X4807,bool),fun(fun(X4807,fun(X4806,bool)),fun(fun(X4807,X4806),bool)),pi(X4807,X4806),X4810),X4809))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_Pi__mono])])])]) ).

cnf(i_0_1595,plain,
    ( ti(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1198]) ).

cnf(i_0_1596,plain,
    ( ti(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1198]) ).

fof(i_0_1597,plain,
    ! [X6246,X6247,X6248] :
      ( ~ linordered_ring(X6246)
      | ~ hBOOL(hAPP(X6246,bool,hAPP(X6246,fun(X6246,bool),ord_less(X6246),hAPP(X6246,X6246,hAPP(X6246,fun(X6246,X6246),plus_plus(X6246),hAPP(X6246,X6246,hAPP(X6246,fun(X6246,X6246),times_times(X6246),X6247),X6247)),hAPP(X6246,X6246,hAPP(X6246,fun(X6246,X6246),times_times(X6246),X6248),X6248))),zero_zero(X6246))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1199])])]) ).

fof(i_0_1598,plain,
    ! [X4860,X4861,X4862,X4863,X4864,X4865] :
      ( ( ~ hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4863),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4864),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(X4861,bool),bool,hAPP(X4861,fun(fun(X4861,bool),bool),member(X4861),esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)),X4865)) )
      & ( ~ hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4864),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4863),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(X4861,bool),bool,hAPP(X4861,fun(fun(X4861,bool),bool),member(X4861),esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)),X4865)) )
      & ( ~ hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4863),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4864),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hAPP(X4861,X4860,X4863,esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)) != hAPP(X4861,X4860,X4864,esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)) )
      & ( ~ hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4864),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hBOOL(hAPP(fun(fun(X4861,X4860),bool),bool,hAPP(fun(X4861,X4860),fun(fun(fun(X4861,X4860),bool),bool),member(fun(X4861,X4860)),X4863),hAPP(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool),hAPP(fun(X4861,bool),fun(fun(X4861,fun(X4860,bool)),fun(fun(X4861,X4860),bool)),pi(X4861,X4860),X4865),X4862)))
        | hAPP(X4861,X4860,X4863,esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)) != hAPP(X4861,X4860,X4864,esk67_6(X4860,X4861,X4862,X4863,X4864,X4865)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_Pi__cong])])])]) ).

fof(i_0_1599,plain,
    ! [X7103,X7104,X7105,X7106] : hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_sup_sup(fun(X7103,bool)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_sup_sup(fun(X7103,bool)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_inf_inf(fun(X7103,bool)),X7104),X7105)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_inf_inf(fun(X7103,bool)),X7105),X7106))),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_inf_inf(fun(X7103,bool)),X7106),X7104)) = hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_inf_inf(fun(X7103,bool)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_inf_inf(fun(X7103,bool)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_sup_sup(fun(X7103,bool)),X7104),X7105)),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_sup_sup(fun(X7103,bool)),X7105),X7106))),hAPP(fun(X7103,bool),fun(X7103,bool),hAPP(fun(X7103,bool),fun(fun(X7103,bool),fun(X7103,bool)),semilattice_sup_sup(fun(X7103,bool)),X7106),X7104)),
    inference(variable_rename,[status(thm)],[fact_886_Un__Int__crazy]) ).

fof(i_0_1600,plain,
    ! [X5783,X5784,X5785,X5786,X5787] :
      ( ( hBOOL(hAPP(fun(X5784,bool),bool,hAPP(X5784,fun(fun(X5784,bool),bool),member(X5784),esk132_5(X5783,X5784,X5785,X5786,X5787)),X5787))
        | hBOOL(hAPP(fun(fun(X5784,X5783),bool),bool,hAPP(fun(X5784,X5783),fun(fun(fun(X5784,X5783),bool),bool),member(fun(X5784,X5783)),hAPP(fun(X5784,bool),fun(X5784,X5783),hAPP(fun(X5784,X5783),fun(fun(X5784,bool),fun(X5784,X5783)),restrict(X5784,X5783),X5785),X5787)),hAPP(fun(X5784,fun(X5783,bool)),fun(fun(X5784,X5783),bool),hAPP(fun(X5784,bool),fun(fun(X5784,fun(X5783,bool)),fun(fun(X5784,X5783),bool)),pi(X5784,X5783),X5787),X5786))) )
      & ( ~ hBOOL(hAPP(fun(X5783,bool),bool,hAPP(X5783,fun(fun(X5783,bool),bool),member(X5783),hAPP(X5784,X5783,X5785,esk132_5(X5783,X5784,X5785,X5786,X5787))),hAPP(X5784,fun(X5783,bool),X5786,esk132_5(X5783,X5784,X5785,X5786,X5787))))
        | hBOOL(hAPP(fun(fun(X5784,X5783),bool),bool,hAPP(fun(X5784,X5783),fun(fun(fun(X5784,X5783),bool),bool),member(fun(X5784,X5783)),hAPP(fun(X5784,bool),fun(X5784,X5783),hAPP(fun(X5784,X5783),fun(fun(X5784,bool),fun(X5784,X5783)),restrict(X5784,X5783),X5785),X5787)),hAPP(fun(X5784,fun(X5783,bool)),fun(fun(X5784,X5783),bool),hAPP(fun(X5784,bool),fun(fun(X5784,fun(X5783,bool)),fun(fun(X5784,X5783),bool)),pi(X5784,X5783),X5787),X5786))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_559_restrictI])])])]) ).

cnf(i_0_1601,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),esk22_4(X1,X2,X3,X4)),esk23_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),esk22_4(X1,X2,X3,X4)),esk23_4(X1,X2,X3,X4))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1200]) ).

fof(i_0_1602,plain,
    ! [X6289,X6290,X6291,X6292,X6293,X6294] :
      ( ( hBOOL(hAPP(fun(X6289,bool),bool,hAPP(X6289,fun(fun(X6289,bool),bool),member(X6289),esk137_6(X6289,X6290,X6291,X6292,X6293,X6294)),X6294))
        | hAPP(fun(X6289,bool),X6290,hAPP(X6290,fun(fun(X6289,bool),X6290),hAPP(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290)),hAPP(fun(X6290,fun(X6290,X6290)),fun(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290))),finite_fold_image(X6290,X6289),times_times(X6290)),X6292),X6291),X6294) = hAPP(fun(X6289,bool),X6290,hAPP(X6290,fun(fun(X6289,bool),X6290),hAPP(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290)),hAPP(fun(X6290,fun(X6290,X6290)),fun(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290))),finite_fold_image(X6290,X6289),times_times(X6290)),X6293),X6291),X6294)
        | ~ hBOOL(hAPP(fun(X6289,bool),bool,finite_finite_1(X6289),X6294))
        | ~ ab_semigroup_mult(X6290) )
      & ( hAPP(X6289,X6290,X6292,esk137_6(X6289,X6290,X6291,X6292,X6293,X6294)) != hAPP(X6289,X6290,X6293,esk137_6(X6289,X6290,X6291,X6292,X6293,X6294))
        | hAPP(fun(X6289,bool),X6290,hAPP(X6290,fun(fun(X6289,bool),X6290),hAPP(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290)),hAPP(fun(X6290,fun(X6290,X6290)),fun(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290))),finite_fold_image(X6290,X6289),times_times(X6290)),X6292),X6291),X6294) = hAPP(fun(X6289,bool),X6290,hAPP(X6290,fun(fun(X6289,bool),X6290),hAPP(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290)),hAPP(fun(X6290,fun(X6290,X6290)),fun(fun(X6289,X6290),fun(X6290,fun(fun(X6289,bool),X6290))),finite_fold_image(X6290,X6289),times_times(X6290)),X6293),X6291),X6294)
        | ~ hBOOL(hAPP(fun(X6289,bool),bool,finite_finite_1(X6289),X6294))
        | ~ ab_semigroup_mult(X6290) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_701_fold__image__cong])])])])]) ).

fof(i_0_1603,plain,
    ! [X4905,X4906,X4907] :
      ( ( ~ hBOOL(hAPP(fun(X4905,bool),bool,finite_finite_1(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),collect(X4905),X4907)))
        | hBOOL(hAPP(fun(X4905,bool),bool,finite_finite_1(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),collect(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),hAPP(fun(X4905,fun(bool,bool)),fun(fun(X4905,bool),fun(X4905,bool)),combs(X4905,bool,bool),hAPP(fun(X4905,bool),fun(X4905,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4905,bool),fun(X4905,fun(bool,bool))),combb(bool,fun(bool,bool),X4905),fconj),X4907)),X4906)))) )
      & ( ~ hBOOL(hAPP(fun(X4905,bool),bool,finite_finite_1(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),collect(X4905),X4906)))
        | hBOOL(hAPP(fun(X4905,bool),bool,finite_finite_1(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),collect(X4905),hAPP(fun(X4905,bool),fun(X4905,bool),hAPP(fun(X4905,fun(bool,bool)),fun(fun(X4905,bool),fun(X4905,bool)),combs(X4905,bool,bool),hAPP(fun(X4905,bool),fun(X4905,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4905,bool),fun(X4905,fun(bool,bool))),combb(bool,fun(bool,bool),X4905),fconj),X4907)),X4906)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_284_finite__Collect__conjI])])]) ).

fof(i_0_1604,plain,
    ! [X4997,X4998] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk75_2(X4997,X4998)),hAPP(nat,nat,X4998,esk75_2(X4997,X4998))))
      | 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)),X4998)),X4997)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_314_finite__less__ub])])]) ).

cnf(i_0_1605,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

fof(i_0_1606,plain,
    ! [X6511,X6512,X6513,X6514,X6515,X6516,X6517,X6518] :
      ( ~ hBOOL(hAPP(fun(fun(X6511,X6512),fun(fun(X6511,bool),X6512)),bool,hAPP(X6512,fun(fun(fun(X6511,X6512),fun(fun(X6511,bool),X6512)),bool),hAPP(fun(X6512,fun(X6512,X6512)),fun(X6512,fun(fun(fun(X6511,X6512),fun(fun(X6511,bool),X6512)),bool)),finite_folding_image(X6512,X6511),X6516),X6517),X6518))
      | ~ hBOOL(hAPP(fun(X6511,bool),bool,finite_finite_1(X6511),X6515))
      | hAPP(fun(X6511,bool),X6512,hAPP(fun(X6511,X6512),fun(fun(X6511,bool),X6512),X6518,hAPP(fun(X6511,X6512),fun(X6511,X6512),hAPP(fun(X6511,fun(X6512,X6512)),fun(fun(X6511,X6512),fun(X6511,X6512)),combs(X6511,X6512,X6512),hAPP(fun(X6511,X6512),fun(X6511,fun(X6512,X6512)),hAPP(fun(X6512,fun(X6512,X6512)),fun(fun(X6511,X6512),fun(X6511,fun(X6512,X6512))),combb(X6512,fun(X6512,X6512),X6511),X6516),X6513)),X6514)),X6515) = hAPP(X6512,X6512,hAPP(X6512,fun(X6512,X6512),X6516,hAPP(fun(X6511,bool),X6512,hAPP(fun(X6511,X6512),fun(fun(X6511,bool),X6512),X6518,X6513),X6515)),hAPP(fun(X6511,bool),X6512,hAPP(fun(X6511,X6512),fun(fun(X6511,bool),X6512),X6518,X6514),X6515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_742_folding__image_Odistrib])]) ).

cnf(i_0_1607,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X3)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1608,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1609,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1610,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1611,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1612,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1613,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1614,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

fof(i_0_1615,plain,
    ! [X4867,X4868,X4869,X4870,X4871] :
      ( ( hBOOL(hAPP(fun(X4868,bool),bool,hAPP(X4868,fun(fun(X4868,bool),bool),member(X4868),esk68_5(X4867,X4868,X4869,X4870,X4871)),X4871))
        | hBOOL(hAPP(fun(fun(X4868,X4867),bool),bool,hAPP(fun(X4868,X4867),fun(fun(fun(X4868,X4867),bool),bool),member(fun(X4868,X4867)),X4869),hAPP(fun(X4868,fun(X4867,bool)),fun(fun(X4868,X4867),bool),hAPP(fun(X4868,bool),fun(fun(X4868,fun(X4867,bool)),fun(fun(X4868,X4867),bool)),pi(X4868,X4867),X4871),X4870))) )
      & ( ~ hBOOL(hAPP(fun(X4867,bool),bool,hAPP(X4867,fun(fun(X4867,bool),bool),member(X4867),hAPP(X4868,X4867,X4869,esk68_5(X4867,X4868,X4869,X4870,X4871))),hAPP(X4868,fun(X4867,bool),X4870,esk68_5(X4867,X4868,X4869,X4870,X4871))))
        | hBOOL(hAPP(fun(fun(X4868,X4867),bool),bool,hAPP(fun(X4868,X4867),fun(fun(fun(X4868,X4867),bool),bool),member(fun(X4868,X4867)),X4869),hAPP(fun(X4868,fun(X4867,bool)),fun(fun(X4868,X4867),bool),hAPP(fun(X4868,bool),fun(fun(X4868,fun(X4867,bool)),fun(fun(X4868,X4867),bool)),pi(X4868,X4867),X4871),X4870))) ) ),
    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_1616,plain,
    ! [X4399,X4400,X4401,X4402,X4403] :
      ( ( hBOOL(hAPP(fun(X4400,bool),bool,hAPP(X4400,fun(fun(X4400,bool),bool),member(X4400),esk33_5(X4399,X4400,X4401,X4402,X4403)),X4403))
        | hBOOL(hAPP(fun(fun(X4400,X4399),bool),bool,hAPP(fun(X4400,X4399),fun(fun(fun(X4400,X4399),bool),bool),member(fun(X4400,X4399)),X4401),hAPP(fun(X4400,fun(X4399,bool)),fun(fun(X4400,X4399),bool),hAPP(fun(X4400,bool),fun(fun(X4400,fun(X4399,bool)),fun(fun(X4400,X4399),bool)),pi(X4400,X4399),X4403),X4402))) )
      & ( ~ hBOOL(hAPP(fun(X4399,bool),bool,hAPP(X4399,fun(fun(X4399,bool),bool),member(X4399),hAPP(X4400,X4399,X4401,esk33_5(X4399,X4400,X4401,X4402,X4403))),hAPP(X4400,fun(X4399,bool),X4402,esk33_5(X4399,X4400,X4401,X4402,X4403))))
        | hBOOL(hAPP(fun(fun(X4400,X4399),bool),bool,hAPP(fun(X4400,X4399),fun(fun(fun(X4400,X4399),bool),bool),member(fun(X4400,X4399)),X4401),hAPP(fun(X4400,fun(X4399,bool)),fun(fun(X4400,X4399),bool),hAPP(fun(X4400,bool),fun(fun(X4400,fun(X4399,bool)),fun(fun(X4400,X4399),bool)),pi(X4400,X4399),X4403),X4402))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_Pi__I])])])]) ).

fof(i_0_1617,plain,
    ! [X7230,X7231,X7232,X7233,X7234] : hBOOL(hAPP(fun(X7230,bool),bool,hAPP(fun(X7230,bool),fun(fun(X7230,bool),bool),ord_less_eq(fun(X7230,bool)),hAPP(fun(X7231,bool),fun(X7230,bool),hAPP(fun(X7231,X7230),fun(fun(X7231,bool),fun(X7230,bool)),image(X7231,X7230),X7232),hAPP(fun(X7231,bool),fun(X7231,bool),hAPP(fun(X7231,bool),fun(fun(X7231,bool),fun(X7231,bool)),semilattice_inf_inf(fun(X7231,bool)),X7233),X7234))),hAPP(fun(X7230,bool),fun(X7230,bool),hAPP(fun(X7230,bool),fun(fun(X7230,bool),fun(X7230,bool)),semilattice_inf_inf(fun(X7230,bool)),hAPP(fun(X7231,bool),fun(X7230,bool),hAPP(fun(X7231,X7230),fun(fun(X7231,bool),fun(X7230,bool)),image(X7231,X7230),X7232),X7233)),hAPP(fun(X7231,bool),fun(X7230,bool),hAPP(fun(X7231,X7230),fun(fun(X7231,bool),fun(X7230,bool)),image(X7231,X7230),X7232),X7234)))),
    inference(variable_rename,[status(thm)],[fact_918_image__Int__subset]) ).

cnf(i_0_1618,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(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)),X5)),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))))
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1201]) ).

fof(i_0_1619,plain,
    ! [X5691,X5692] :
      ( ( ~ hBOOL(hAPP(X5691,bool,hAPP(X5691,fun(X5691,bool),ord_less(X5691),hAPP(X5691,X5691,hAPP(X5691,fun(X5691,X5691),plus_plus(X5691),hAPP(X5691,X5691,hAPP(X5691,fun(X5691,X5691),plus_plus(X5691),one_one(X5691)),X5692)),X5692)),zero_zero(X5691)))
        | hBOOL(hAPP(X5691,bool,hAPP(X5691,fun(X5691,bool),ord_less(X5691),X5692),zero_zero(X5691)))
        | ~ hBOOL(hAPP(fun(X5691,bool),bool,hAPP(X5691,fun(fun(X5691,bool),bool),member(X5691),X5692),ring_1_Ints(X5691)))
        | ~ linordered_idom(X5691) )
      & ( ~ hBOOL(hAPP(X5691,bool,hAPP(X5691,fun(X5691,bool),ord_less(X5691),X5692),zero_zero(X5691)))
        | hBOOL(hAPP(X5691,bool,hAPP(X5691,fun(X5691,bool),ord_less(X5691),hAPP(X5691,X5691,hAPP(X5691,fun(X5691,X5691),plus_plus(X5691),hAPP(X5691,X5691,hAPP(X5691,fun(X5691,X5691),plus_plus(X5691),one_one(X5691)),X5692)),X5692)),zero_zero(X5691)))
        | ~ hBOOL(hAPP(fun(X5691,bool),bool,hAPP(X5691,fun(fun(X5691,bool),bool),member(X5691),X5692),ring_1_Ints(X5691)))
        | ~ linordered_idom(X5691) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_532_Ints__odd__less__0])])])]) ).

fof(i_0_1620,plain,
    ! [X6274,X6275,X6276,X6277,X6278,X6279] :
      ( ~ linord1278240602ring_1(X6274)
      | ~ hBOOL(hAPP(X6274,bool,hAPP(X6274,fun(X6274,bool),ord_less_eq(X6274),X6278),X6279))
      | ~ hBOOL(hAPP(X6274,bool,hAPP(X6274,fun(X6274,bool),ord_less_eq(X6274),X6277),X6279))
      | ~ hBOOL(hAPP(X6274,bool,hAPP(X6274,fun(X6274,bool),ord_less_eq(X6274),zero_zero(X6274)),X6276))
      | ~ hBOOL(hAPP(X6274,bool,hAPP(X6274,fun(X6274,bool),ord_less_eq(X6274),zero_zero(X6274)),X6275))
      | hAPP(X6274,X6274,hAPP(X6274,fun(X6274,X6274),plus_plus(X6274),X6276),X6275) != one_one(X6274)
      | hBOOL(hAPP(X6274,bool,hAPP(X6274,fun(X6274,bool),ord_less_eq(X6274),hAPP(X6274,X6274,hAPP(X6274,fun(X6274,X6274),plus_plus(X6274),hAPP(X6274,X6274,hAPP(X6274,fun(X6274,X6274),times_times(X6274),X6276),X6278)),hAPP(X6274,X6274,hAPP(X6274,fun(X6274,X6274),times_times(X6274),X6275),X6277))),X6279)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_698_convex__bound__le])])]) ).

fof(i_0_1621,plain,
    ! [X5856,X5857,X5858,X5859,X5860,X5861] :
      ( ~ linord626643107strict(X5856)
      | ~ hBOOL(hAPP(X5856,bool,hAPP(X5856,fun(X5856,bool),ord_less(X5856),X5860),X5861))
      | ~ hBOOL(hAPP(X5856,bool,hAPP(X5856,fun(X5856,bool),ord_less(X5856),X5859),X5861))
      | ~ hBOOL(hAPP(X5856,bool,hAPP(X5856,fun(X5856,bool),ord_less_eq(X5856),zero_zero(X5856)),X5858))
      | ~ hBOOL(hAPP(X5856,bool,hAPP(X5856,fun(X5856,bool),ord_less_eq(X5856),zero_zero(X5856)),X5857))
      | hAPP(X5856,X5856,hAPP(X5856,fun(X5856,X5856),plus_plus(X5856),X5858),X5857) != one_one(X5856)
      | hBOOL(hAPP(X5856,bool,hAPP(X5856,fun(X5856,bool),ord_less(X5856),hAPP(X5856,X5856,hAPP(X5856,fun(X5856,X5856),plus_plus(X5856),hAPP(X5856,X5856,hAPP(X5856,fun(X5856,X5856),times_times(X5856),X5858),X5860)),hAPP(X5856,X5856,hAPP(X5856,fun(X5856,X5856),times_times(X5856),X5857),X5859))),X5861)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_570_convex__bound__lt])])]) ).

fof(i_0_1622,plain,
    ! [X5789,X5790,X5791,X5792,X5793] :
      ( ( hBOOL(hAPP(fun(X5790,bool),bool,hAPP(X5790,fun(fun(X5790,bool),bool),member(X5790),esk133_5(X5789,X5790,X5791,X5792,X5793)),X5793))
        | hBOOL(hAPP(fun(fun(X5790,X5789),bool),bool,hAPP(fun(X5790,X5789),fun(fun(fun(X5790,X5789),bool),bool),member(fun(X5790,X5789)),hAPP(fun(X5790,bool),fun(X5790,X5789),hAPP(fun(X5790,X5789),fun(fun(X5790,bool),fun(X5790,X5789)),restrict(X5790,X5789),X5791),X5793)),hAPP(fun(X5790,fun(X5789,bool)),fun(fun(X5790,X5789),bool),hAPP(fun(X5790,bool),fun(fun(X5790,fun(X5789,bool)),fun(fun(X5790,X5789),bool)),pi(X5790,X5789),X5793),hAPP(fun(X5789,bool),fun(X5790,fun(X5789,bool)),combk(fun(X5789,bool),X5790),X5792)))) )
      & ( ~ hBOOL(hAPP(fun(X5789,bool),bool,hAPP(X5789,fun(fun(X5789,bool),bool),member(X5789),hAPP(X5790,X5789,X5791,esk133_5(X5789,X5790,X5791,X5792,X5793))),X5792))
        | hBOOL(hAPP(fun(fun(X5790,X5789),bool),bool,hAPP(fun(X5790,X5789),fun(fun(fun(X5790,X5789),bool),bool),member(fun(X5790,X5789)),hAPP(fun(X5790,bool),fun(X5790,X5789),hAPP(fun(X5790,X5789),fun(fun(X5790,bool),fun(X5790,X5789)),restrict(X5790,X5789),X5791),X5793)),hAPP(fun(X5790,fun(X5789,bool)),fun(fun(X5790,X5789),bool),hAPP(fun(X5790,bool),fun(fun(X5790,fun(X5789,bool)),fun(fun(X5790,X5789),bool)),pi(X5790,X5789),X5793),hAPP(fun(X5789,bool),fun(X5790,fun(X5789,bool)),combk(fun(X5789,bool),X5790),X5792)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_560_restrict__in__funcset])])])]) ).

fof(i_0_1623,plain,
    ! [X7053,X7054,X7055,X7056] :
      ( ~ lattice(X7053)
      | hBOOL(hAPP(X7053,bool,hAPP(X7053,fun(X7053,bool),ord_less_eq(X7053),hAPP(X7053,X7053,hAPP(X7053,fun(X7053,X7053),semilattice_sup_sup(X7053),hAPP(X7053,X7053,hAPP(X7053,fun(X7053,X7053),semilattice_inf_inf(X7053),X7054),X7055)),hAPP(X7053,X7053,hAPP(X7053,fun(X7053,X7053),semilattice_inf_inf(X7053),X7054),X7056))),hAPP(X7053,X7053,hAPP(X7053,fun(X7053,X7053),semilattice_inf_inf(X7053),X7054),hAPP(X7053,X7053,hAPP(X7053,fun(X7053,X7053),semilattice_sup_sup(X7053),X7055),X7056)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_873_distrib__inf__le])])]) ).

cnf(i_0_1624,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1625,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X3)),X5))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1626,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X2),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1627,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X5),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1628,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X3),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1629,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1630,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

cnf(i_0_1631,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk147_6(X2,X1,X3,X4,X5,X6)),X6))
    | 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),X4),X6)
    | ti(fun(X1,bool),X5) != ti(fun(X1,bool),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_1202]) ).

fof(i_0_1632,plain,
    ! [X6738,X6739,X6740] : hAPP(fun(X6738,bool),fun(X6738,bool),hAPP(fun(X6738,bool),fun(fun(X6738,bool),fun(X6738,bool)),semilattice_sup_sup(fun(X6738,bool)),X6739),X6740) = hAPP(fun(X6738,bool),fun(X6738,bool),collect(X6738),hAPP(fun(X6738,bool),fun(X6738,bool),hAPP(fun(X6738,fun(bool,bool)),fun(fun(X6738,bool),fun(X6738,bool)),combs(X6738,bool,bool),hAPP(fun(X6738,bool),fun(X6738,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X6738,bool),fun(X6738,fun(bool,bool))),combb(bool,fun(bool,bool),X6738),fdisj),hAPP(fun(X6738,bool),fun(X6738,bool),hAPP(fun(X6738,fun(fun(X6738,bool),bool)),fun(fun(X6738,bool),fun(X6738,bool)),combc(X6738,fun(X6738,bool),bool),member(X6738)),X6739))),hAPP(fun(X6738,bool),fun(X6738,bool),hAPP(fun(X6738,fun(fun(X6738,bool),bool)),fun(fun(X6738,bool),fun(X6738,bool)),combc(X6738,fun(X6738,bool),bool),member(X6738)),X6740))),
    inference(variable_rename,[status(thm)],[fact_792_Un__def]) ).

fof(i_0_1633,plain,
    ! [X7189,X7190,X7191] : hAPP(fun(X7189,bool),fun(X7189,bool),hAPP(fun(X7189,bool),fun(fun(X7189,bool),fun(X7189,bool)),semilattice_inf_inf(fun(X7189,bool)),X7190),X7191) = hAPP(fun(X7189,bool),fun(X7189,bool),collect(X7189),hAPP(fun(X7189,bool),fun(X7189,bool),hAPP(fun(X7189,fun(bool,bool)),fun(fun(X7189,bool),fun(X7189,bool)),combs(X7189,bool,bool),hAPP(fun(X7189,bool),fun(X7189,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7189,bool),fun(X7189,fun(bool,bool))),combb(bool,fun(bool,bool),X7189),fconj),hAPP(fun(X7189,bool),fun(X7189,bool),hAPP(fun(X7189,fun(fun(X7189,bool),bool)),fun(fun(X7189,bool),fun(X7189,bool)),combc(X7189,fun(X7189,bool),bool),member(X7189)),X7190))),hAPP(fun(X7189,bool),fun(X7189,bool),hAPP(fun(X7189,fun(fun(X7189,bool),bool)),fun(fun(X7189,bool),fun(X7189,bool)),combc(X7189,fun(X7189,bool),bool),member(X7189)),X7191))),
    inference(variable_rename,[status(thm)],[fact_907_Int__def]) ).

fof(i_0_1634,plain,
    ! [X7029,X7030,X7031,X7032,X7033] :
      ( ~ comm_monoid_add(X7029)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7032),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7033),one_one(nat))))
      | hAPP(fun(nat,bool),X7029,hAPP(fun(nat,X7029),fun(fun(nat,bool),X7029),big_co1399186613setsum(nat,X7029),X7030),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7032),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7033),X7031))) = hAPP(X7029,X7029,hAPP(X7029,fun(X7029,X7029),plus_plus(X7029),hAPP(fun(nat,bool),X7029,hAPP(fun(nat,X7029),fun(fun(nat,bool),X7029),big_co1399186613setsum(nat,X7029),X7030),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7032),X7033))),hAPP(fun(nat,bool),X7029,hAPP(fun(nat,X7029),fun(fun(nat,bool),X7029),big_co1399186613setsum(nat,X7029),X7030),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7033),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7033),X7031)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_867_setsum__ub__add__nat])])]) ).

fof(i_0_1635,plain,
    ! [X4956,X4957,X4958,X4959,X4960,X4961,X4962,X4963] :
      ( ~ hBOOL(hAPP(fun(fun(X4956,bool),X4957),bool,hAPP(fun(X4956,X4957),fun(fun(fun(X4956,bool),X4957),bool),hAPP(X4957,fun(fun(X4956,X4957),fun(fun(fun(X4956,bool),X4957),bool)),hAPP(fun(X4957,fun(X4957,X4957)),fun(X4957,fun(fun(X4956,X4957),fun(fun(fun(X4956,bool),X4957),bool))),finite908156982e_idem(X4957,X4956),X4960),X4961),X4962),X4963))
      | ~ hBOOL(hAPP(fun(X4956,bool),bool,finite_finite_1(X4956),X4959))
      | ~ hBOOL(hAPP(fun(X4956,bool),bool,hAPP(fun(X4956,bool),fun(fun(X4956,bool),bool),ord_less_eq(fun(X4956,bool)),X4958),X4959))
      | hAPP(X4957,X4957,hAPP(X4957,fun(X4957,X4957),X4960,hAPP(fun(X4956,bool),X4957,X4963,X4958)),hAPP(fun(X4956,bool),X4957,X4963,X4959)) = hAPP(fun(X4956,bool),X4957,X4963,X4959) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_306_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_1636,plain,
    ! [X6814,X6815,X6816,X6817,X6818,X6819,X6820,X6821] :
      ( ~ hBOOL(hAPP(fun(fun(X6814,bool),X6815),bool,hAPP(fun(X6814,X6815),fun(fun(fun(X6814,bool),X6815),bool),hAPP(X6815,fun(fun(X6814,X6815),fun(fun(fun(X6814,bool),X6815),bool)),hAPP(fun(X6815,fun(X6815,X6815)),fun(X6815,fun(fun(X6814,X6815),fun(fun(fun(X6814,bool),X6815),bool))),finite908156982e_idem(X6815,X6814),X6818),X6819),X6820),X6821))
      | ~ hBOOL(hAPP(fun(X6814,bool),bool,finite_finite_1(X6814),X6817))
      | ~ hBOOL(hAPP(fun(X6814,bool),bool,finite_finite_1(X6814),X6816))
      | hAPP(fun(X6814,bool),X6815,X6821,hAPP(fun(X6814,bool),fun(X6814,bool),hAPP(fun(X6814,bool),fun(fun(X6814,bool),fun(X6814,bool)),semilattice_sup_sup(fun(X6814,bool)),X6817),X6816)) = hAPP(X6815,X6815,hAPP(X6815,fun(X6815,X6815),X6818,hAPP(fun(X6814,bool),X6815,X6821,X6817)),hAPP(fun(X6814,bool),X6815,X6821,X6816)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_808_folding__image__simple__idem_Ounion__idem])]) ).

fof(i_0_1637,plain,
    ! [X4853,X4854,X4855,X4856,X4857] :
      ( ( hBOOL(hAPP(fun(X4854,bool),bool,hAPP(X4854,fun(fun(X4854,bool),bool),member(X4854),esk65_5(X4853,X4854,X4855,X4856,X4857)),X4857))
        | hBOOL(hAPP(fun(fun(X4854,X4853),bool),bool,hAPP(fun(X4854,X4853),fun(fun(fun(X4854,X4853),bool),bool),member(fun(X4854,X4853)),X4855),hAPP(fun(X4854,fun(X4853,bool)),fun(fun(X4854,X4853),bool),hAPP(fun(X4854,bool),fun(fun(X4854,fun(X4853,bool)),fun(fun(X4854,X4853),bool)),pi(X4854,X4853),X4857),hAPP(fun(X4853,bool),fun(X4854,fun(X4853,bool)),combk(fun(X4853,bool),X4854),X4856)))) )
      & ( ~ hBOOL(hAPP(fun(X4853,bool),bool,hAPP(X4853,fun(fun(X4853,bool),bool),member(X4853),hAPP(X4854,X4853,X4855,esk65_5(X4853,X4854,X4855,X4856,X4857))),X4856))
        | hBOOL(hAPP(fun(fun(X4854,X4853),bool),bool,hAPP(fun(X4854,X4853),fun(fun(fun(X4854,X4853),bool),bool),member(fun(X4854,X4853)),X4855),hAPP(fun(X4854,fun(X4853,bool)),fun(fun(X4854,X4853),bool),hAPP(fun(X4854,bool),fun(fun(X4854,fun(X4853,bool)),fun(fun(X4854,X4853),bool)),pi(X4854,X4853),X4857),hAPP(fun(X4853,bool),fun(X4854,fun(X4853,bool)),combk(fun(X4853,bool),X4854),X4856)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_funcsetI])])])]) ).

fof(i_0_1638,plain,
    ! [X4987,X4988,X4989,X4990,X4991,X4992,X4993,X4994] :
      ( ~ hBOOL(hAPP(fun(fun(X4987,bool),X4988),bool,hAPP(fun(X4987,X4988),fun(fun(fun(X4987,bool),X4988),bool),hAPP(X4988,fun(fun(X4987,X4988),fun(fun(fun(X4987,bool),X4988),bool)),hAPP(fun(X4988,fun(X4988,X4988)),fun(X4988,fun(fun(X4987,X4988),fun(fun(fun(X4987,bool),X4988),bool))),finite908156982e_idem(X4988,X4987),X4991),X4992),X4993),X4994))
      | ~ hBOOL(hAPP(fun(X4987,bool),bool,finite_finite_1(X4987),X4990))
      | ~ hBOOL(hAPP(fun(X4987,bool),bool,hAPP(X4987,fun(fun(X4987,bool),bool),member(X4987),X4989),X4990))
      | hAPP(X4988,X4988,hAPP(X4988,fun(X4988,X4988),X4991,hAPP(X4987,X4988,X4993,X4989)),hAPP(fun(X4987,bool),X4988,X4994,X4990)) = hAPP(fun(X4987,bool),X4988,X4994,X4990) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_312_folding__image__simple__idem_Oin__idem])]) ).

cnf(i_0_1639,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1640,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1641,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1642,plain,
    ( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X3)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X3)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1643,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1644,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ti(arrow_2142409994le_alt,X2) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

fof(i_0_1645,plain,
    ! [X4884,X4885,X4886,X4887,X4888,X4889] :
      ( ~ hBOOL(hAPP(fun(fun(X4884,X4885),bool),bool,hAPP(fun(X4884,X4885),fun(fun(fun(X4884,X4885),bool),bool),member(fun(X4884,X4885)),X4887),hAPP(fun(X4884,fun(X4885,bool)),fun(fun(X4884,X4885),bool),hAPP(fun(X4884,bool),fun(fun(X4884,fun(X4885,bool)),fun(fun(X4884,X4885),bool)),pi(X4884,X4885),X4888),hAPP(fun(X4885,bool),fun(X4884,fun(X4885,bool)),combk(fun(X4885,bool),X4884),X4889))))
      | ~ hBOOL(hAPP(fun(X4884,bool),bool,hAPP(fun(X4884,X4885),fun(fun(X4884,bool),bool),inj_on(X4884,X4885),X4887),X4888))
      | ~ hBOOL(hAPP(fun(fun(X4885,X4884),bool),bool,hAPP(fun(X4885,X4884),fun(fun(fun(X4885,X4884),bool),bool),member(fun(X4885,X4884)),X4886),hAPP(fun(X4885,fun(X4884,bool)),fun(fun(X4885,X4884),bool),hAPP(fun(X4885,bool),fun(fun(X4885,fun(X4884,bool)),fun(fun(X4885,X4884),bool)),pi(X4885,X4884),X4889),hAPP(fun(X4884,bool),fun(X4885,fun(X4884,bool)),combk(fun(X4884,bool),X4885),X4888))))
      | ~ hBOOL(hAPP(fun(X4885,bool),bool,hAPP(fun(X4885,X4884),fun(fun(X4885,bool),bool),inj_on(X4885,X4884),X4886),X4889))
      | ~ hBOOL(hAPP(fun(X4884,bool),bool,finite_finite_1(X4884),X4888))
      | ~ hBOOL(hAPP(fun(X4885,bool),bool,finite_finite_1(X4885),X4889))
      | hAPP(fun(X4884,bool),nat,finite_card(X4884),X4888) = hAPP(fun(X4885,bool),nat,finite_card(X4885),X4889) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_277_card__bij])]) ).

cnf(i_0_1646,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1647,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X5),X4)))
    | ti(arrow_2142409994le_alt,X5) = ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1648,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
    | ti(X1,X2) != zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1198]) ).

cnf(i_0_1649,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X3),X2)))
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

cnf(i_0_1650,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

fof(i_0_1651,plain,
    ! [X5685,X5686,X5687,X5688,X5689] :
      ( ( hBOOL(hAPP(fun(X5686,bool),bool,hAPP(X5686,fun(fun(X5686,bool),bool),member(X5686),esk131_5(X5685,X5686,X5687,X5688,X5689)),X5689))
        | hBOOL(hAPP(fun(X5685,bool),bool,hAPP(fun(X5685,bool),fun(fun(X5685,bool),bool),ord_less_eq(fun(X5685,bool)),hAPP(fun(X5686,bool),fun(X5685,bool),hAPP(fun(X5686,X5685),fun(fun(X5686,bool),fun(X5685,bool)),image(X5686,X5685),X5687),X5689)),X5688)) )
      & ( ~ hBOOL(hAPP(fun(X5685,bool),bool,hAPP(X5685,fun(fun(X5685,bool),bool),member(X5685),hAPP(X5686,X5685,X5687,esk131_5(X5685,X5686,X5687,X5688,X5689))),X5688))
        | hBOOL(hAPP(fun(X5685,bool),bool,hAPP(fun(X5685,bool),fun(fun(X5685,bool),bool),ord_less_eq(fun(X5685,bool)),hAPP(fun(X5686,bool),fun(X5685,bool),hAPP(fun(X5686,X5685),fun(fun(X5686,bool),fun(X5685,bool)),image(X5686,X5685),X5687),X5689)),X5688)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_530_image__subsetI])])])]) ).

cnf(i_0_1652,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

cnf(i_0_1653,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),esk22_4(X1,X2,X3,X4)),esk23_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),esk22_4(X1,X2,X3,X4)),esk23_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_1200]) ).

cnf(i_0_1654,plain,
    ( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1655,plain,
    ( ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X5)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

fof(i_0_1656,plain,
    ! [X3995,X3996,X3997,X3998,X4000,X4004] :
      ( ( ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X3995))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3996),arrow_301600364e_Prof))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3997),X3998)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3996,esk14_4(X3995,X3996,X3997,X3998))))
        | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3997),X3998)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3995,X3996))) )
      & ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk15_1(X4000)),arrow_301600364e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X4000)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X4000)),esk17_1(X4000))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk15_1(X4000),X4004)))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X4000)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X4000)),esk17_1(X4000))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4000,esk15_1(X4000))))
        | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X4000)) ) ),
    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_1657,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

fof(i_0_1658,plain,
    ! [X5562,X5563,X5564,X5565,X5566,X5567] :
      ( ~ hBOOL(hAPP(fun(X5562,bool),bool,hAPP(fun(X5562,X5563),fun(fun(X5562,bool),bool),inj_on(X5562,X5563),X5566),X5567))
      | ~ hBOOL(hAPP(fun(X5563,bool),bool,hAPP(fun(X5563,bool),fun(fun(X5563,bool),bool),ord_less_eq(fun(X5563,bool)),hAPP(fun(X5562,bool),fun(X5563,bool),hAPP(fun(X5562,X5563),fun(fun(X5562,bool),fun(X5563,bool)),image(X5562,X5563),X5566),X5567)),X5565))
      | ~ hBOOL(hAPP(fun(X5563,bool),bool,hAPP(fun(X5563,X5562),fun(fun(X5563,bool),bool),inj_on(X5563,X5562),X5564),X5565))
      | ~ hBOOL(hAPP(fun(X5562,bool),bool,hAPP(fun(X5562,bool),fun(fun(X5562,bool),bool),ord_less_eq(fun(X5562,bool)),hAPP(fun(X5563,bool),fun(X5562,bool),hAPP(fun(X5563,X5562),fun(fun(X5563,bool),fun(X5562,bool)),image(X5563,X5562),X5564),X5565)),X5567))
      | ~ hBOOL(hAPP(fun(X5562,bool),bool,finite_finite_1(X5562),X5567))
      | ~ hBOOL(hAPP(fun(X5563,bool),bool,finite_finite_1(X5563),X5565))
      | hAPP(fun(X5562,bool),nat,finite_card(X5562),X5567) = hAPP(fun(X5563,bool),nat,finite_card(X5563),X5565) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_508_card__bij__eq])]) ).

fof(i_0_1659,plain,
    ! [X7057,X7058,X7059,X7060] :
      ( ~ lattice(X7057)
      | hBOOL(hAPP(X7057,bool,hAPP(X7057,fun(X7057,bool),ord_less_eq(X7057),hAPP(X7057,X7057,hAPP(X7057,fun(X7057,X7057),semilattice_sup_sup(X7057),X7058),hAPP(X7057,X7057,hAPP(X7057,fun(X7057,X7057),semilattice_inf_inf(X7057),X7059),X7060))),hAPP(X7057,X7057,hAPP(X7057,fun(X7057,X7057),semilattice_inf_inf(X7057),hAPP(X7057,X7057,hAPP(X7057,fun(X7057,X7057),semilattice_sup_sup(X7057),X7058),X7059)),hAPP(X7057,X7057,hAPP(X7057,fun(X7057,X7057),semilattice_sup_sup(X7057),X7058),X7060)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_874_distrib__sup__le])])]) ).

cnf(i_0_1660,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_1203]) ).

fof(i_0_1661,plain,
    ! [X7513,X7514,X7515,X7516,X7517] :
      ( ~ comm_monoid_add(X7514)
      | ~ hBOOL(hAPP(fun(X7513,bool),bool,finite_finite_1(X7513),X7517))
      | hAPP(fun(X7513,bool),X7514,hAPP(fun(X7513,X7514),fun(fun(X7513,bool),X7514),big_co1399186613setsum(X7513,X7514),hAPP(fun(X7513,X7514),fun(X7513,X7514),hAPP(fun(X7513,fun(X7514,X7514)),fun(fun(X7513,X7514),fun(X7513,X7514)),combs(X7513,X7514,X7514),hAPP(fun(X7513,X7514),fun(X7513,fun(X7514,X7514)),hAPP(fun(X7514,fun(X7514,X7514)),fun(fun(X7513,X7514),fun(X7513,fun(X7514,X7514))),combb(X7514,fun(X7514,X7514),X7513),plus_plus(X7514)),X7515)),X7516)),X7517) = hAPP(X7514,X7514,hAPP(X7514,fun(X7514,X7514),plus_plus(X7514),hAPP(fun(X7513,bool),X7514,hAPP(fun(X7513,X7514),fun(fun(X7513,bool),X7514),big_co1399186613setsum(X7513,X7514),X7515),X7517)),hAPP(fun(X7513,bool),X7514,hAPP(fun(X7513,X7514),fun(fun(X7513,bool),X7514),big_co1399186613setsum(X7513,X7514),X7516),X7517)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_989_setsum_Odistrib])])]) ).

fof(i_0_1662,plain,
    ! [X7468,X7469,X7470,X7471,X7472] :
      ( ~ comm_monoid_add(X7469)
      | hAPP(fun(X7468,bool),X7469,hAPP(fun(X7468,X7469),fun(fun(X7468,bool),X7469),big_co1399186613setsum(X7468,X7469),hAPP(fun(X7468,X7469),fun(X7468,X7469),hAPP(fun(X7468,fun(X7469,X7469)),fun(fun(X7468,X7469),fun(X7468,X7469)),combs(X7468,X7469,X7469),hAPP(fun(X7468,X7469),fun(X7468,fun(X7469,X7469)),hAPP(fun(X7469,fun(X7469,X7469)),fun(fun(X7468,X7469),fun(X7468,fun(X7469,X7469))),combb(X7469,fun(X7469,X7469),X7468),plus_plus(X7469)),X7470)),X7471)),X7472) = hAPP(X7469,X7469,hAPP(X7469,fun(X7469,X7469),plus_plus(X7469),hAPP(fun(X7468,bool),X7469,hAPP(fun(X7468,X7469),fun(fun(X7468,bool),X7469),big_co1399186613setsum(X7468,X7469),X7470),X7472)),hAPP(fun(X7468,bool),X7469,hAPP(fun(X7468,X7469),fun(fun(X7468,bool),X7469),big_co1399186613setsum(X7468,X7469),X7471),X7472)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_980_setsum__addf])])]) ).

cnf(i_0_1663,plain,
    ( 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),X4),X6)
    | hAPP(X1,X2,X3,esk147_6(X2,X1,X3,X4,X5,X6)) != hAPP(X1,X2,X4,esk147_6(X2,X1,X3,X4,X5,X6))
    | ti(fun(X1,bool),X5) != ti(fun(X1,bool),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_1202]) ).

fof(i_0_1664,plain,
    ! [X5653,X5654,X5655,X5656,X5657] :
      ( ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(X5654,fun(fun(X5654,bool),bool),member(X5654),esk124_5(X5653,X5654,X5655,X5656,X5657)),X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(X5654,fun(fun(X5654,bool),bool),member(X5654),esk124_5(X5653,X5654,X5655,X5656,X5657)),X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(X5654,fun(fun(X5654,bool),bool),member(X5654),esk125_5(X5653,X5654,X5655,X5656,X5657)),X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(X5654,fun(fun(X5654,bool),bool),member(X5654),esk125_5(X5653,X5654,X5655,X5656,X5657)),X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk124_5(X5653,X5654,X5655,X5656,X5657))) != hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk125_5(X5653,X5654,X5655,X5656,X5657)))
        | hAPP(X5654,X5653,X5655,esk124_5(X5653,X5654,X5655,X5656,X5657)) != hAPP(X5654,X5653,X5655,esk125_5(X5653,X5654,X5655,X5656,X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk124_5(X5653,X5654,X5655,X5656,X5657))) != hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk125_5(X5653,X5654,X5655,X5656,X5657)))
        | hAPP(X5654,X5653,X5655,esk124_5(X5653,X5654,X5655,X5656,X5657)) != hAPP(X5654,X5653,X5655,esk125_5(X5653,X5654,X5655,X5656,X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk124_5(X5653,X5654,X5655,X5656,X5657))) = hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk125_5(X5653,X5654,X5655,X5656,X5657)))
        | hAPP(X5654,X5653,X5655,esk124_5(X5653,X5654,X5655,X5656,X5657)) = hAPP(X5654,X5653,X5655,esk125_5(X5653,X5654,X5655,X5656,X5657)) )
      & ( ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),X5657))
        | hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5653),fun(fun(X5654,bool),bool),inj_on(X5654,X5653),X5655),hAPP(fun(X5654,bool),fun(X5654,bool),hAPP(fun(X5654,X5654),fun(fun(X5654,bool),fun(X5654,bool)),image(X5654,X5654),X5656),X5657)))
        | ~ hBOOL(hAPP(fun(X5654,bool),bool,hAPP(fun(X5654,X5654),fun(fun(X5654,bool),bool),inj_on(X5654,X5654),X5656),X5657))
        | hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk124_5(X5653,X5654,X5655,X5656,X5657))) = hAPP(X5654,X5653,X5655,hAPP(X5654,X5654,X5656,esk125_5(X5653,X5654,X5655,X5656,X5657)))
        | hAPP(X5654,X5653,X5655,esk124_5(X5653,X5654,X5655,X5656,X5657)) = hAPP(X5654,X5653,X5655,esk125_5(X5653,X5654,X5655,X5656,X5657)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_525_inj__on__image__iff])])])]) ).

cnf(i_0_1665,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

fof(i_0_1666,plain,
    ! [X6570,X6571,X6572,X6573,X6574] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X6570,nat,X6572,X6573)),hAPP(X6570,nat,X6572,X6574)))
      | ~ hBOOL(hAPP(fun(product_prod(X6570,X6570),bool),bool,hAPP(product_prod(X6570,X6570),fun(fun(product_prod(X6570,X6570),bool),bool),member(product_prod(X6570,X6570)),hAPP(X6570,product_prod(X6570,X6570),hAPP(X6570,fun(X6570,product_prod(X6570,X6570)),product_Pair(X6570,X6570),X6573),X6574)),X6571))
      | hBOOL(hAPP(fun(product_prod(X6570,X6570),bool),bool,hAPP(product_prod(X6570,X6570),fun(fun(product_prod(X6570,X6570),bool),bool),member(product_prod(X6570,X6570)),hAPP(X6570,product_prod(X6570,X6570),hAPP(X6570,fun(X6570,product_prod(X6570,X6570)),product_Pair(X6570,X6570),X6573),X6574)),hAPP(fun(product_prod(X6570,X6570),bool),fun(product_prod(X6570,X6570),bool),hAPP(fun(X6570,nat),fun(fun(product_prod(X6570,X6570),bool),fun(product_prod(X6570,X6570),bool)),mlex_prod(X6570),X6572),X6571))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_753_mlex__leq])]) ).

fof(i_0_1667,plain,
    ! [X7478,X7479,X7480,X7481,X7482] :
      ( ~ semiring_0(X7479)
      | hAPP(X7479,X7479,hAPP(X7479,fun(X7479,X7479),times_times(X7479),hAPP(fun(X7478,bool),X7479,hAPP(fun(X7478,X7479),fun(fun(X7478,bool),X7479),big_co1399186613setsum(X7478,X7479),X7480),X7481)),X7482) = hAPP(fun(X7478,bool),X7479,hAPP(fun(X7478,X7479),fun(fun(X7478,bool),X7479),big_co1399186613setsum(X7478,X7479),hAPP(X7479,fun(X7478,X7479),hAPP(fun(X7478,fun(X7479,X7479)),fun(X7479,fun(X7478,X7479)),combc(X7478,X7479,X7479),hAPP(fun(X7478,X7479),fun(X7478,fun(X7479,X7479)),hAPP(fun(X7479,fun(X7479,X7479)),fun(fun(X7478,X7479),fun(X7478,fun(X7479,X7479))),combb(X7479,fun(X7479,X7479),X7478),times_times(X7479)),X7480)),X7482)),X7481) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_982_setsum__left__distrib])])]) ).

cnf(i_0_1668,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1204]) ).

cnf(i_0_1669,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1205]) ).

fof(i_0_1670,plain,
    ! [X5534,X5535,X5536,X5537] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X5534,bool),nat,finite_card(X5534),hAPP(fun(X5535,bool),fun(X5534,bool),hAPP(fun(X5535,X5534),fun(fun(X5535,bool),fun(X5534,bool)),image(X5535,X5534),X5536),X5537))),hAPP(fun(X5535,bool),nat,finite_card(X5535),X5537)))
      | ~ hBOOL(hAPP(fun(X5535,bool),bool,hAPP(fun(X5535,X5534),fun(fun(X5535,bool),bool),inj_on(X5535,X5534),X5536),X5537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1206])]) ).

cnf(i_0_1671,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
    | ti(X1,X2) != zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1207]) ).

cnf(i_0_1672,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]) ).

fof(i_0_1673,plain,
    ! [X5735,X5736,X5737,X5738,X5739,X5740] :
      ( ~ hBOOL(hAPP(fun(X5735,bool),bool,hAPP(fun(X5735,X5736),fun(fun(X5735,bool),bool),inj_on(X5735,X5736),X5739),X5740))
      | ~ hBOOL(hAPP(fun(X5736,bool),bool,hAPP(X5736,fun(fun(X5736,bool),bool),member(X5736),X5738),hAPP(fun(X5735,bool),fun(X5736,bool),hAPP(fun(X5735,X5736),fun(fun(X5735,bool),fun(X5736,bool)),image(X5735,X5736),X5739),X5740)))
      | ~ hBOOL(hAPP(fun(X5735,bool),bool,hAPP(fun(X5735,bool),fun(fun(X5735,bool),bool),ord_less_eq(fun(X5735,bool)),X5740),X5737))
      | hBOOL(hAPP(fun(X5735,bool),bool,hAPP(X5735,fun(fun(X5735,bool),bool),member(X5735),hAPP(X5736,X5735,hAPP(fun(X5735,X5736),fun(X5736,X5735),hAPP(fun(X5735,bool),fun(fun(X5735,X5736),fun(X5736,X5735)),the_inv_into(X5735,X5736),X5740),X5739),X5738)),X5737)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_547_the__inv__into__into])]) ).

cnf(i_0_1674,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1208]) ).

fof(i_0_1675,plain,
    ! [X5579,X5580,X5581,X5582,X5583] :
      ( ( hBOOL(hAPP(fun(X5580,bool),bool,hAPP(X5580,fun(fun(X5580,bool),bool),member(X5580),esk108_5(X5579,X5580,X5581,X5582,X5583)),hAPP(fun(X5579,bool),fun(X5580,bool),hAPP(fun(X5579,X5580),fun(fun(X5579,bool),fun(X5580,bool)),image(X5579,X5580),X5583),top_top(fun(X5579,bool)))))
        | hBOOL(hAPP(X5579,bool,X5582,X5581))
        | ~ hBOOL(hAPP(fun(X5579,bool),bool,hAPP(fun(X5579,X5580),fun(fun(X5579,bool),bool),inj_on(X5579,X5580),X5583),top_top(fun(X5579,bool)))) )
      & ( ~ hBOOL(hAPP(X5579,bool,X5582,hAPP(X5580,X5579,hAPP(fun(X5579,X5580),fun(X5580,X5579),hAPP(fun(X5579,bool),fun(fun(X5579,X5580),fun(X5580,X5579)),hilbert_inv_into(X5579,X5580),top_top(fun(X5579,bool))),X5583),esk108_5(X5579,X5580,X5581,X5582,X5583))))
        | hBOOL(hAPP(X5579,bool,X5582,X5581))
        | ~ hBOOL(hAPP(fun(X5579,bool),bool,hAPP(fun(X5579,X5580),fun(fun(X5579,bool),bool),inj_on(X5579,X5580),X5583),top_top(fun(X5579,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_511_inj__transfer])])])]) ).

fof(i_0_1676,plain,
    ! [X6166,X6167,X6168] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6166)),X6167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6166)),X6168)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6167),X6168)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6167),X6168))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6166)),X6167)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6166)),X6168))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_668_Suc__mult__le__cancel1])]) ).

fof(i_0_1677,plain,
    ! [X6159,X6160,X6161] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6159)),X6160)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6159)),X6161)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6160),X6161)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6160),X6161))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6159)),X6160)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6159)),X6161))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_665_Suc__mult__less__cancel1])]) ).

fof(i_0_1678,plain,
    ! [X4038,X4039,X4040] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4040),arrow_1568854078le_Lin))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4038),X4039)),X4040))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4039),X4038)),X4040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1209])]) ).

fof(i_0_1679,plain,
    ! [X4689,X4690,X4691] :
      ( ( ~ hBOOL(hAPP(fun(X4689,bool),bool,hAPP(fun(X4689,bool),fun(fun(X4689,bool),bool),ord_less_eq(fun(X4689,bool)),hAPP(fun(X4689,bool),fun(X4689,bool),hAPP(fun(X4689,fun(fun(X4689,bool),bool)),fun(fun(X4689,bool),fun(X4689,bool)),combc(X4689,fun(X4689,bool),bool),member(X4689)),X4690)),hAPP(fun(X4689,bool),fun(X4689,bool),hAPP(fun(X4689,fun(fun(X4689,bool),bool)),fun(fun(X4689,bool),fun(X4689,bool)),combc(X4689,fun(X4689,bool),bool),member(X4689)),X4691)))
        | hBOOL(hAPP(fun(X4689,bool),bool,hAPP(fun(X4689,bool),fun(fun(X4689,bool),bool),ord_less_eq(fun(X4689,bool)),X4690),X4691)) )
      & ( ~ hBOOL(hAPP(fun(X4689,bool),bool,hAPP(fun(X4689,bool),fun(fun(X4689,bool),bool),ord_less_eq(fun(X4689,bool)),X4690),X4691))
        | hBOOL(hAPP(fun(X4689,bool),bool,hAPP(fun(X4689,bool),fun(fun(X4689,bool),bool),ord_less_eq(fun(X4689,bool)),hAPP(fun(X4689,bool),fun(X4689,bool),hAPP(fun(X4689,fun(fun(X4689,bool),bool)),fun(fun(X4689,bool),fun(X4689,bool)),combc(X4689,fun(X4689,bool),bool),member(X4689)),X4690)),hAPP(fun(X4689,bool),fun(X4689,bool),hAPP(fun(X4689,fun(fun(X4689,bool),bool)),fun(fun(X4689,bool),fun(X4689,bool)),combc(X4689,fun(X4689,bool),bool),member(X4689)),X4691))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_pred__subset__eq])]) ).

fof(i_0_1680,plain,
    ! [X6501,X6502,X6503,X6504,X6505,X6506,X6507,X6508] :
      ( ~ hBOOL(hAPP(fun(fun(X6501,X6502),fun(fun(X6501,bool),X6502)),bool,hAPP(X6502,fun(fun(fun(X6501,X6502),fun(fun(X6501,bool),X6502)),bool),hAPP(fun(X6502,fun(X6502,X6502)),fun(X6502,fun(fun(fun(X6501,X6502),fun(fun(X6501,bool),X6502)),bool)),finite_folding_image(X6502,X6501),X6506),X6507),X6508))
      | ~ hBOOL(hAPP(fun(X6501,bool),bool,finite_finite_1(X6501),X6505))
      | ~ hBOOL(hAPP(fun(X6501,bool),bool,hAPP(fun(X6501,X6501),fun(fun(X6501,bool),bool),inj_on(X6501,X6501),X6504),X6505))
      | hAPP(fun(X6501,bool),X6502,hAPP(fun(X6501,X6502),fun(fun(X6501,bool),X6502),X6508,X6503),hAPP(fun(X6501,bool),fun(X6501,bool),hAPP(fun(X6501,X6501),fun(fun(X6501,bool),fun(X6501,bool)),image(X6501,X6501),X6504),X6505)) = hAPP(fun(X6501,bool),X6502,hAPP(fun(X6501,X6502),fun(fun(X6501,bool),X6502),X6508,hAPP(fun(X6501,X6501),fun(X6501,X6502),hAPP(fun(X6501,X6502),fun(fun(X6501,X6501),fun(X6501,X6502)),comp(X6501,X6502,X6501),X6503),X6504)),X6505) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_739_folding__image_Oreindex])]) ).

fof(i_0_1681,plain,
    ! [X6179,X6180,X6181,X6182,X6183,X6184] : hBOOL(hAPP(fun(fun(X6179,X6180),bool),bool,hAPP(fun(X6179,X6180),fun(fun(fun(X6179,X6180),bool),bool),member(fun(X6179,X6180)),hAPP(fun(X6179,X6181),fun(X6179,X6180),hAPP(fun(X6181,X6180),fun(fun(X6179,X6181),fun(X6179,X6180)),hAPP(fun(X6179,bool),fun(fun(X6181,X6180),fun(fun(X6179,X6181),fun(X6179,X6180))),compose(X6179,X6181,X6180),X6182),X6183),X6184)),hAPP(fun(X6179,bool),fun(fun(X6179,X6180),bool),extensional(X6179,X6180),X6182))),
    inference(variable_rename,[status(thm)],[fact_672_compose__extensional]) ).

cnf(i_0_1682,plain,
    ( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X4),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X5)),X3) = ti(fun(X1,X2),X3)
    | ~ 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(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1210]) ).

fof(i_0_1683,plain,
    ! [X5492,X5493,X5494,X5495,X5496] :
      ( ~ hBOOL(hAPP(fun(X5493,bool),bool,finite_finite_1(X5493),hAPP(fun(X5494,bool),fun(X5493,bool),hAPP(fun(X5494,X5493),fun(fun(X5494,bool),fun(X5493,bool)),image(X5494,X5493),X5496),top_top(fun(X5494,bool)))))
      | hBOOL(hAPP(fun(X5492,bool),bool,finite_finite_1(X5492),hAPP(fun(X5494,bool),fun(X5492,bool),hAPP(fun(X5494,X5492),fun(fun(X5494,bool),fun(X5492,bool)),image(X5494,X5492),hAPP(fun(X5494,X5493),fun(X5494,X5492),hAPP(fun(X5493,X5492),fun(fun(X5494,X5493),fun(X5494,X5492)),combb(X5493,X5492,X5494),X5495),X5496)),top_top(fun(X5494,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_490_finite__range__imageI])]) ).

fof(i_0_1684,plain,
    ! [X6373,X6374,X6375,X6376,X6377,X6378,X6379] :
      ( ~ ab_semigroup_mult(X6375)
      | ~ hBOOL(hAPP(fun(X6374,bool),bool,finite_finite_1(X6374),X6379))
      | ~ hBOOL(hAPP(fun(X6374,bool),bool,hAPP(fun(X6374,X6373),fun(fun(X6374,bool),bool),inj_on(X6374,X6373),X6378),X6379))
      | hAPP(fun(X6373,bool),X6375,hAPP(X6375,fun(fun(X6373,bool),X6375),hAPP(fun(X6373,X6375),fun(X6375,fun(fun(X6373,bool),X6375)),hAPP(fun(X6375,fun(X6375,X6375)),fun(fun(X6373,X6375),fun(X6375,fun(fun(X6373,bool),X6375))),finite_fold_image(X6375,X6373),times_times(X6375)),X6376),X6377),hAPP(fun(X6374,bool),fun(X6373,bool),hAPP(fun(X6374,X6373),fun(fun(X6374,bool),fun(X6373,bool)),image(X6374,X6373),X6378),X6379)) = hAPP(fun(X6374,bool),X6375,hAPP(X6375,fun(fun(X6374,bool),X6375),hAPP(fun(X6374,X6375),fun(X6375,fun(fun(X6374,bool),X6375)),hAPP(fun(X6375,fun(X6375,X6375)),fun(fun(X6374,X6375),fun(X6375,fun(fun(X6374,bool),X6375))),finite_fold_image(X6375,X6374),times_times(X6375)),hAPP(fun(X6374,X6373),fun(X6374,X6375),hAPP(fun(X6373,X6375),fun(fun(X6374,X6373),fun(X6374,X6375)),comp(X6373,X6375,X6374),X6376),X6378)),X6377),X6379) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_718_fold__image__reindex])])]) ).

cnf(i_0_1685,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

cnf(i_0_1686,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

cnf(i_0_1687,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1196]) ).

cnf(i_0_1688,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | ti(arrow_2142409994le_alt,X4) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) != ti(arrow_2142409994le_alt,X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1197]) ).

fof(i_0_1689,plain,
    ! [X6535,X6536,X6537] :
      ( ( hBOOL(hAPP(fun(X6535,bool),bool,hAPP(fun(X6535,bool),fun(fun(X6535,bool),bool),ord_less(fun(X6535,bool)),X6536),X6537))
        | ~ hBOOL(hAPP(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool,hAPP(product_prod(fun(X6535,bool),fun(X6535,bool)),fun(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool),member(product_prod(fun(X6535,bool),fun(X6535,bool))),hAPP(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool)),hAPP(fun(X6535,bool),fun(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool))),product_Pair(fun(X6535,bool),fun(X6535,bool)),X6536),X6537)),finite_psubset(X6535))) )
      & ( hBOOL(hAPP(fun(X6535,bool),bool,finite_finite_1(X6535),X6537))
        | ~ hBOOL(hAPP(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool,hAPP(product_prod(fun(X6535,bool),fun(X6535,bool)),fun(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool),member(product_prod(fun(X6535,bool),fun(X6535,bool))),hAPP(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool)),hAPP(fun(X6535,bool),fun(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool))),product_Pair(fun(X6535,bool),fun(X6535,bool)),X6536),X6537)),finite_psubset(X6535))) )
      & ( ~ hBOOL(hAPP(fun(X6535,bool),bool,hAPP(fun(X6535,bool),fun(fun(X6535,bool),bool),ord_less(fun(X6535,bool)),X6536),X6537))
        | ~ hBOOL(hAPP(fun(X6535,bool),bool,finite_finite_1(X6535),X6537))
        | hBOOL(hAPP(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool,hAPP(product_prod(fun(X6535,bool),fun(X6535,bool)),fun(fun(product_prod(fun(X6535,bool),fun(X6535,bool)),bool),bool),member(product_prod(fun(X6535,bool),fun(X6535,bool))),hAPP(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool)),hAPP(fun(X6535,bool),fun(fun(X6535,bool),product_prod(fun(X6535,bool),fun(X6535,bool))),product_Pair(fun(X6535,bool),fun(X6535,bool)),X6536),X6537)),finite_psubset(X6535))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_746_in__finite__psubset])])]) ).

fof(i_0_1690,plain,
    ! [X6519,X6520,X6521,X6522,X6523,X6524,X6525] :
      ( ~ hBOOL(hAPP(fun(fun(X6519,X6520),fun(fun(X6519,bool),X6520)),bool,hAPP(X6520,fun(fun(fun(X6519,X6520),fun(fun(X6519,bool),X6520)),bool),hAPP(fun(X6520,fun(X6520,X6520)),fun(X6520,fun(fun(fun(X6519,X6520),fun(fun(X6519,bool),X6520)),bool)),finite_folding_image(X6520,X6519),X6523),X6524),X6525))
      | ~ hBOOL(hAPP(fun(X6519,bool),bool,finite_finite_1(X6519),X6522))
      | hAPP(fun(X6519,bool),X6520,hAPP(fun(X6519,X6520),fun(fun(X6519,bool),X6520),X6525,X6521),X6522) = hAPP(fun(X6519,bool),X6520,hAPP(X6520,fun(fun(X6519,bool),X6520),hAPP(fun(X6519,X6520),fun(X6520,fun(fun(X6519,bool),X6520)),hAPP(fun(X6520,fun(X6520,X6520)),fun(fun(X6519,X6520),fun(X6520,fun(fun(X6519,bool),X6520))),finite_fold_image(X6520,X6519),X6523),X6521),X6524),X6522) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_744_folding__image_Oeq__fold])]) ).

cnf(i_0_1691,plain,
    ( hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X4),X3),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X4)) = ti(fun(X1,X2),X3)
    | ~ 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(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1213]) ).

fof(i_0_1692,plain,
    ! [X5416,X5417,X5418,X5419,X5420] :
      ( ~ hBOOL(hAPP(fun(X5416,bool),bool,hAPP(X5416,fun(fun(X5416,bool),bool),member(X5416),X5418),hAPP(fun(X5417,bool),fun(X5416,bool),hAPP(fun(X5417,X5416),fun(fun(X5417,bool),fun(X5416,bool)),image(X5417,X5416),X5419),X5420)))
      | hBOOL(hAPP(fun(X5417,bool),bool,hAPP(X5417,fun(fun(X5417,bool),bool),member(X5417),hAPP(X5416,X5417,hAPP(fun(X5417,X5416),fun(X5416,X5417),hAPP(fun(X5417,bool),fun(fun(X5417,X5416),fun(X5416,X5417)),hilbert_inv_into(X5417,X5416),X5420),X5419),X5418)),X5420)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_475_inv__into__into])]) ).

fof(i_0_1693,plain,
    ! [X4816,X4817,X4818] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X4816,X4817,X4818)),esk62_3(X4816,X4817,X4818)))
        | 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,X4818,X4816)),X4817)),hAPP(nat,nat,X4818,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4816),X4817)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X4818,esk61_3(X4816,X4817,X4818))),hAPP(nat,nat,X4818,esk62_3(X4816,X4817,X4818))))
        | 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,X4818,X4816)),X4817)),hAPP(nat,nat,X4818,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4816),X4817)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_mono__nat__linear__lb])])])]) ).

fof(i_0_1694,plain,
    ! [X5256,X5257,X5258,X5259] :
      ( ( ~ hBOOL(hAPP(X5256,bool,hAPP(X5256,fun(X5256,bool),ord_less(X5256),hAPP(nat,X5256,X5259,X5257)),hAPP(nat,X5256,X5259,X5258)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5257),X5258))
        | ~ hBOOL(hAPP(X5256,bool,hAPP(X5256,fun(X5256,bool),ord_less(X5256),hAPP(nat,X5256,X5259,esk91_4(X5256,X5257,X5258,X5259))),hAPP(nat,X5256,X5259,hAPP(nat,nat,suc,esk91_4(X5256,X5257,X5258,X5259)))))
        | ~ order(X5256) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5257),X5258))
        | hBOOL(hAPP(X5256,bool,hAPP(X5256,fun(X5256,bool),ord_less(X5256),hAPP(nat,X5256,X5259,X5257)),hAPP(nat,X5256,X5259,X5258)))
        | ~ hBOOL(hAPP(X5256,bool,hAPP(X5256,fun(X5256,bool),ord_less(X5256),hAPP(nat,X5256,X5259,esk91_4(X5256,X5257,X5258,X5259))),hAPP(nat,X5256,X5259,hAPP(nat,nat,suc,esk91_4(X5256,X5257,X5258,X5259)))))
        | ~ order(X5256) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_lift__Suc__mono__less__iff])])])])]) ).

cnf(i_0_1695,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

cnf(i_0_1696,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

cnf(i_0_1697,plain,
    ( ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

cnf(i_0_1698,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X4)
    | ti(arrow_2142409994le_alt,X2) = ti(arrow_2142409994le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

fof(i_0_1699,plain,
    ! [X5502,X5503,X5504,X5505,X5506] :
      ( ~ hBOOL(hAPP(fun(fun(X5502,X5503),bool),bool,hAPP(fun(X5502,X5503),fun(fun(fun(X5502,X5503),bool),bool),member(fun(X5502,X5503)),X5504),hAPP(fun(X5502,fun(X5503,bool)),fun(fun(X5502,X5503),bool),hAPP(fun(X5502,bool),fun(fun(X5502,fun(X5503,bool)),fun(fun(X5502,X5503),bool)),pi(X5502,X5503),X5505),hAPP(fun(X5503,bool),fun(X5502,fun(X5503,bool)),combk(fun(X5503,bool),X5502),X5506))))
      | hBOOL(hAPP(fun(X5503,bool),bool,hAPP(fun(X5503,bool),fun(fun(X5503,bool),bool),ord_less_eq(fun(X5503,bool)),hAPP(fun(X5502,bool),fun(X5503,bool),hAPP(fun(X5502,X5503),fun(fun(X5502,bool),fun(X5503,bool)),image(X5502,X5503),X5504),X5505)),X5506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_492_funcset__image])]) ).

fof(i_0_1700,plain,
    ! [X6987,X6988,X6989,X6990,X6991,X6992] :
      ( ~ hBOOL(hAPP(X6987,bool,hAPP(X6988,fun(X6987,bool),hAPP(fun(X6988,fun(X6987,bool)),fun(X6988,fun(X6987,bool)),hAPP(fun(X6988,fun(X6987,bool)),fun(fun(X6988,fun(X6987,bool)),fun(X6988,fun(X6987,bool))),semilattice_sup_sup(fun(X6988,fun(X6987,bool))),X6989),X6990),X6991),X6992))
      | hBOOL(hAPP(X6987,bool,hAPP(X6988,fun(X6987,bool),X6989,X6991),X6992))
      | hBOOL(hAPP(X6987,bool,hAPP(X6988,fun(X6987,bool),X6990,X6991),X6992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1214])]) ).

fof(i_0_1701,plain,
    ! [X5517,X5518,X5519,X5520,X5521] :
      ( ( ~ hBOOL(hAPP(fun(X5518,bool),bool,hAPP(fun(X5518,bool),fun(fun(X5518,bool),bool),ord_less_eq(fun(X5518,bool)),hAPP(fun(X5517,bool),fun(X5518,bool),hAPP(fun(X5517,X5518),fun(fun(X5517,bool),fun(X5518,bool)),image(X5517,X5518),X5521),X5519)),hAPP(fun(X5517,bool),fun(X5518,bool),hAPP(fun(X5517,X5518),fun(fun(X5517,bool),fun(X5518,bool)),image(X5517,X5518),X5521),X5520)))
        | hBOOL(hAPP(fun(X5517,bool),bool,hAPP(fun(X5517,bool),fun(fun(X5517,bool),bool),ord_less_eq(fun(X5517,bool)),X5519),X5520))
        | ~ hBOOL(hAPP(fun(X5517,bool),bool,hAPP(fun(X5517,X5518),fun(fun(X5517,bool),bool),inj_on(X5517,X5518),X5521),top_top(fun(X5517,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X5517,bool),bool,hAPP(fun(X5517,bool),fun(fun(X5517,bool),bool),ord_less_eq(fun(X5517,bool)),X5519),X5520))
        | hBOOL(hAPP(fun(X5518,bool),bool,hAPP(fun(X5518,bool),fun(fun(X5518,bool),bool),ord_less_eq(fun(X5518,bool)),hAPP(fun(X5517,bool),fun(X5518,bool),hAPP(fun(X5517,X5518),fun(fun(X5517,bool),fun(X5518,bool)),image(X5517,X5518),X5521),X5519)),hAPP(fun(X5517,bool),fun(X5518,bool),hAPP(fun(X5517,X5518),fun(fun(X5517,bool),fun(X5518,bool)),image(X5517,X5518),X5521),X5520)))
        | ~ hBOOL(hAPP(fun(X5517,bool),bool,hAPP(fun(X5517,X5518),fun(fun(X5517,bool),bool),inj_on(X5517,X5518),X5521),top_top(fun(X5517,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_497_inj__image__subset__iff])])]) ).

fof(i_0_1702,plain,
    ! [X5251,X5252,X5253,X5254] :
      ( ~ order(X5251)
      | ~ hBOOL(hAPP(X5251,bool,hAPP(X5251,fun(X5251,bool),ord_less_eq(X5251),hAPP(nat,X5251,X5254,esk90_4(X5251,X5252,X5253,X5254))),hAPP(nat,X5251,X5254,hAPP(nat,nat,suc,esk90_4(X5251,X5252,X5253,X5254)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5252),X5253))
      | hBOOL(hAPP(X5251,bool,hAPP(X5251,fun(X5251,bool),ord_less_eq(X5251),hAPP(nat,X5251,X5254,X5252)),hAPP(nat,X5251,X5254,X5253))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_lift__Suc__mono__le])])])]) ).

fof(i_0_1703,plain,
    ! [X5261,X5262,X5263,X5264] :
      ( ~ order(X5261)
      | ~ hBOOL(hAPP(X5261,bool,hAPP(X5261,fun(X5261,bool),ord_less(X5261),hAPP(nat,X5261,X5264,esk92_4(X5261,X5262,X5263,X5264))),hAPP(nat,X5261,X5264,hAPP(nat,nat,suc,esk92_4(X5261,X5262,X5263,X5264)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5262),X5263))
      | hBOOL(hAPP(X5261,bool,hAPP(X5261,fun(X5261,bool),ord_less(X5261),hAPP(nat,X5261,X5264,X5262)),hAPP(nat,X5261,X5264,X5263))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_435_lift__Suc__mono__less])])])]) ).

fof(i_0_1704,plain,
    ! [X7122,X7123,X7124,X7125,X7126] :
      ( ~ comm_monoid_add(X7122)
      | hAPP(fun(nat,bool),X7122,hAPP(fun(nat,X7122),fun(fun(nat,bool),X7122),big_co1399186613setsum(nat,X7122),X7123),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7124),X7125)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7126),X7125))) = hAPP(fun(nat,bool),X7122,hAPP(fun(nat,X7122),fun(fun(nat,bool),X7122),big_co1399186613setsum(nat,X7122),hAPP(fun(nat,nat),fun(nat,X7122),hAPP(fun(nat,X7122),fun(fun(nat,nat),fun(nat,X7122)),combb(nat,X7122,nat),X7123),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X7125))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7124),X7126)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_890_setsum__shift__bounds__nat__ivl])])]) ).

fof(i_0_1705,plain,
    ! [X7113,X7114,X7115,X7116,X7117] :
      ( ~ comm_monoid_add(X7113)
      | hAPP(fun(nat,bool),X7113,hAPP(fun(nat,X7113),fun(fun(nat,bool),X7113),big_co1399186613setsum(nat,X7113),X7114),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7115),X7116)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X7117),X7116))) = hAPP(fun(nat,bool),X7113,hAPP(fun(nat,X7113),fun(fun(nat,bool),X7113),big_co1399186613setsum(nat,X7113),hAPP(fun(nat,nat),fun(nat,X7113),hAPP(fun(nat,X7113),fun(fun(nat,nat),fun(nat,X7113)),combb(nat,X7113,nat),X7114),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X7116))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7115),X7117)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_888_setsum__shift__bounds__cl__nat__ivl])])]) ).

fof(i_0_1706,plain,
    ! [X7545,X7546,X7547,X7548,X7549] :
      ( ~ comm_monoid_add(X7546)
      | ~ hBOOL(hAPP(fun(X7545,bool),bool,finite_finite_1(X7545),X7549))
      | ~ hBOOL(hAPP(fun(X7545,bool),bool,finite_finite_1(X7545),X7548))
      | hAPP(X7546,X7546,hAPP(X7546,fun(X7546,X7546),plus_plus(X7546),hAPP(fun(X7545,bool),X7546,hAPP(fun(X7545,X7546),fun(fun(X7545,bool),X7546),big_co1399186613setsum(X7545,X7546),X7547),hAPP(fun(X7545,bool),fun(X7545,bool),hAPP(fun(X7545,bool),fun(fun(X7545,bool),fun(X7545,bool)),semilattice_sup_sup(fun(X7545,bool)),X7549),X7548))),hAPP(fun(X7545,bool),X7546,hAPP(fun(X7545,X7546),fun(fun(X7545,bool),X7546),big_co1399186613setsum(X7545,X7546),X7547),hAPP(fun(X7545,bool),fun(X7545,bool),hAPP(fun(X7545,bool),fun(fun(X7545,bool),fun(X7545,bool)),semilattice_inf_inf(fun(X7545,bool)),X7549),X7548))) = hAPP(X7546,X7546,hAPP(X7546,fun(X7546,X7546),plus_plus(X7546),hAPP(fun(X7545,bool),X7546,hAPP(fun(X7545,X7546),fun(fun(X7545,bool),X7546),big_co1399186613setsum(X7545,X7546),X7547),X7549)),hAPP(fun(X7545,bool),X7546,hAPP(fun(X7545,X7546),fun(fun(X7545,bool),X7546),big_co1399186613setsum(X7545,X7546),X7547),X7548)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_995_setsum__Un__Int])])]) ).

fof(i_0_1707,plain,
    ! [X6403,X6404,X6405,X6406,X6407,X6408] :
      ( ( ~ hBOOL(hAPP(fun(X6405,bool),bool,hAPP(fun(X6405,X6403),fun(fun(X6405,bool),bool),inj_on(X6405,X6403),X6406),hAPP(fun(X6404,bool),fun(X6405,bool),hAPP(fun(X6404,X6405),fun(fun(X6404,bool),fun(X6405,bool)),image(X6404,X6405),X6407),X6408)))
        | hBOOL(hAPP(fun(X6404,bool),bool,hAPP(fun(X6404,X6403),fun(fun(X6404,bool),bool),inj_on(X6404,X6403),hAPP(fun(X6404,X6405),fun(X6404,X6403),hAPP(fun(X6405,X6403),fun(fun(X6404,X6405),fun(X6404,X6403)),comp(X6405,X6403,X6404),X6406),X6407)),X6408))
        | ~ hBOOL(hAPP(fun(X6404,bool),bool,hAPP(fun(X6404,X6405),fun(fun(X6404,bool),bool),inj_on(X6404,X6405),X6407),X6408)) )
      & ( ~ hBOOL(hAPP(fun(X6404,bool),bool,hAPP(fun(X6404,X6403),fun(fun(X6404,bool),bool),inj_on(X6404,X6403),hAPP(fun(X6404,X6405),fun(X6404,X6403),hAPP(fun(X6405,X6403),fun(fun(X6404,X6405),fun(X6404,X6403)),comp(X6405,X6403,X6404),X6406),X6407)),X6408))
        | hBOOL(hAPP(fun(X6405,bool),bool,hAPP(fun(X6405,X6403),fun(fun(X6405,bool),bool),inj_on(X6405,X6403),X6406),hAPP(fun(X6404,bool),fun(X6405,bool),hAPP(fun(X6404,X6405),fun(fun(X6404,bool),fun(X6405,bool)),image(X6404,X6405),X6407),X6408)))
        | ~ hBOOL(hAPP(fun(X6404,bool),bool,hAPP(fun(X6404,X6405),fun(fun(X6404,bool),bool),inj_on(X6404,X6405),X6407),X6408)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_724_comp__inj__on__iff])])]) ).

fof(i_0_1708,plain,
    ! [X5995,X5996,X5997,X5998,X5999] :
      ( ~ semiring(X5995)
      | hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),plus_plus(X5995),hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),times_times(X5995),X5996),X5997)),hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),plus_plus(X5995),hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),times_times(X5995),X5998),X5997)),X5999)) = hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),plus_plus(X5995),hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),times_times(X5995),hAPP(X5995,X5995,hAPP(X5995,fun(X5995,X5995),plus_plus(X5995),X5996),X5998)),X5997)),X5999) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_617_combine__common__factor])])]) ).

fof(i_0_1709,plain,
    ! [X5490,X5491] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X5490),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X5491),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5491),hAPP(fun(nat,bool),nat,finite_card(nat),X5490)))))
      | X5490 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X5491),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5491),hAPP(fun(nat,bool),nat,finite_card(nat),X5490))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_489_subset__card__intvl__is__intvl])]) ).

cnf(i_0_1710,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_1200]) ).

cnf(i_0_1711,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_1200]) ).

fof(i_0_1712,plain,
    ! [X7431,X7432,X7433,X7434,X7435,X7436] :
      ( ( hBOOL(hAPP(X7431,bool,hAPP(X7432,fun(X7431,bool),X7433,X7435),X7436))
        | ~ hBOOL(hAPP(X7431,bool,hAPP(X7432,fun(X7431,bool),hAPP(fun(X7432,fun(X7431,bool)),fun(X7432,fun(X7431,bool)),hAPP(fun(X7432,fun(X7431,bool)),fun(fun(X7432,fun(X7431,bool)),fun(X7432,fun(X7431,bool))),semilattice_inf_inf(fun(X7432,fun(X7431,bool))),X7433),X7434),X7435),X7436)) )
      & ( hBOOL(hAPP(X7431,bool,hAPP(X7432,fun(X7431,bool),X7434,X7435),X7436))
        | ~ hBOOL(hAPP(X7431,bool,hAPP(X7432,fun(X7431,bool),hAPP(fun(X7432,fun(X7431,bool)),fun(X7432,fun(X7431,bool)),hAPP(fun(X7432,fun(X7431,bool)),fun(fun(X7432,fun(X7431,bool)),fun(X7432,fun(X7431,bool))),semilattice_inf_inf(fun(X7432,fun(X7431,bool))),X7433),X7434),X7435),X7436)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1215])])]) ).

fof(i_0_1713,plain,
    ! [X7449,X7450,X7451,X7452,X7453,X7454] :
      ( ~ hBOOL(hAPP(X7449,bool,hAPP(X7450,fun(X7449,bool),hAPP(fun(X7450,fun(X7449,bool)),fun(X7450,fun(X7449,bool)),hAPP(fun(X7450,fun(X7449,bool)),fun(fun(X7450,fun(X7449,bool)),fun(X7450,fun(X7449,bool))),semilattice_inf_inf(fun(X7450,fun(X7449,bool))),X7451),X7452),X7453),X7454))
      | hBOOL(hAPP(X7449,bool,hAPP(X7450,fun(X7449,bool),X7451,X7453),X7454)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_975_inf2D1])]) ).

fof(i_0_1714,plain,
    ! [X7443,X7444,X7445,X7446,X7447,X7448] :
      ( ~ hBOOL(hAPP(X7443,bool,hAPP(X7444,fun(X7443,bool),hAPP(fun(X7444,fun(X7443,bool)),fun(X7444,fun(X7443,bool)),hAPP(fun(X7444,fun(X7443,bool)),fun(fun(X7444,fun(X7443,bool)),fun(X7444,fun(X7443,bool))),semilattice_inf_inf(fun(X7444,fun(X7443,bool))),X7445),X7446),X7447),X7448))
      | hBOOL(hAPP(X7443,bool,hAPP(X7444,fun(X7443,bool),X7446,X7447),X7448)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_974_inf2D2])]) ).

fof(i_0_1715,plain,
    ! [X4873,X4874,X4875,X4876,X4877] :
      ( ~ hBOOL(hAPP(fun(fun(X4873,X4874),bool),bool,hAPP(fun(X4873,X4874),fun(fun(fun(X4873,X4874),bool),bool),member(fun(X4873,X4874)),X4875),hAPP(fun(X4873,fun(X4874,bool)),fun(fun(X4873,X4874),bool),hAPP(fun(X4873,bool),fun(fun(X4873,fun(X4874,bool)),fun(fun(X4873,X4874),bool)),pi(X4873,X4874),X4876),hAPP(fun(X4874,bool),fun(X4873,fun(X4874,bool)),combk(fun(X4874,bool),X4873),X4877))))
      | ~ hBOOL(hAPP(fun(X4873,bool),bool,hAPP(fun(X4873,X4874),fun(fun(X4873,bool),bool),inj_on(X4873,X4874),X4875),X4876))
      | ~ hBOOL(hAPP(fun(X4874,bool),bool,finite_finite_1(X4874),X4877))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X4873,bool),nat,finite_card(X4873),X4876)),hAPP(fun(X4874,bool),nat,finite_card(X4874),X4877))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_card__inj])]) ).

cnf(i_0_1716,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_1216]) ).

fof(i_0_1717,plain,
    ! [X5573,X5574,X5575,X5576,X5577] :
      ( ( ~ hBOOL(hAPP(fun(X5574,bool),bool,hAPP(fun(X5574,X5573),fun(fun(X5574,bool),bool),inj_on(X5574,X5573),X5577),X5576))
        | ~ hBOOL(hAPP(fun(X5573,bool),bool,hAPP(fun(X5573,bool),fun(fun(X5573,bool),bool),ord_less_eq(fun(X5573,bool)),hAPP(fun(X5574,bool),fun(X5573,bool),hAPP(fun(X5574,X5573),fun(fun(X5574,bool),fun(X5573,bool)),image(X5574,X5573),X5577),X5576)),X5575))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X5574,bool),nat,finite_card(X5574),X5576)),hAPP(fun(X5573,bool),nat,finite_card(X5573),X5575)))
        | ~ hBOOL(hAPP(fun(X5573,bool),bool,finite_finite_1(X5573),X5575))
        | ~ hBOOL(hAPP(fun(X5574,bool),bool,finite_finite_1(X5574),X5576)) )
      & ( hBOOL(hAPP(fun(X5574,bool),bool,hAPP(fun(X5574,X5573),fun(fun(X5574,bool),bool),inj_on(X5574,X5573),esk107_4(X5573,X5574,X5575,X5576)),X5576))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X5574,bool),nat,finite_card(X5574),X5576)),hAPP(fun(X5573,bool),nat,finite_card(X5573),X5575)))
        | ~ hBOOL(hAPP(fun(X5573,bool),bool,finite_finite_1(X5573),X5575))
        | ~ hBOOL(hAPP(fun(X5574,bool),bool,finite_finite_1(X5574),X5576)) )
      & ( hBOOL(hAPP(fun(X5573,bool),bool,hAPP(fun(X5573,bool),fun(fun(X5573,bool),bool),ord_less_eq(fun(X5573,bool)),hAPP(fun(X5574,bool),fun(X5573,bool),hAPP(fun(X5574,X5573),fun(fun(X5574,bool),fun(X5573,bool)),image(X5574,X5573),esk107_4(X5573,X5574,X5575,X5576)),X5576)),X5575))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X5574,bool),nat,finite_card(X5574),X5576)),hAPP(fun(X5573,bool),nat,finite_card(X5573),X5575)))
        | ~ hBOOL(hAPP(fun(X5573,bool),bool,finite_finite_1(X5573),X5575))
        | ~ hBOOL(hAPP(fun(X5574,bool),bool,finite_finite_1(X5574),X5576)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_510_inj__on__iff__card__le])])])])]) ).

fof(i_0_1718,plain,
    ! [X6313,X6314,X6315,X6316] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6313),X6314)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6315),X6314)),X6316)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6313),X6315)),X6314)),X6316),
    inference(variable_rename,[status(thm)],[fact_708_left__add__mult__distrib]) ).

fof(i_0_1719,plain,
    ! [X6649,X6650,X6651,X6652,X6653] :
      ( ( hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6650))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6650),X6651))
        | ~ hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6651),X6653))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6650),X6651))
        | ~ hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less(X6649),X6652),X6650))
        | hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less(X6649),X6651),X6653))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6650),X6651))
        | ~ hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6653))
        | ~ hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6650),X6651))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6653))
        | hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less(X6649),X6652),X6650))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6650))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6651),X6653))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6653))
        | hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) )
      & ( ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less(X6649),X6651),X6653))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6650))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6651),X6653))
        | ~ hBOOL(hAPP(X6649,bool,hAPP(X6649,fun(X6649,bool),ord_less_eq(X6649),X6652),X6653))
        | hBOOL(hAPP(fun(X6649,bool),bool,hAPP(fun(X6649,bool),fun(fun(X6649,bool),bool),ord_less(fun(X6649,bool)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6650),X6651)),hAPP(X6649,fun(X6649,bool),hAPP(X6649,fun(X6649,fun(X6649,bool)),ord_atLeastAtMost(X6649),X6652),X6653)))
        | ~ order(X6649) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1217])])])]) ).

fof(i_0_1720,plain,
    ! [X5568,X5569,X5570,X5571,X5572] :
      ( ~ hBOOL(hAPP(fun(X5568,bool),bool,hAPP(fun(X5568,X5569),fun(fun(X5568,bool),bool),inj_on(X5568,X5569),X5571),X5572))
      | ~ hBOOL(hAPP(fun(X5569,bool),bool,hAPP(fun(X5569,bool),fun(fun(X5569,bool),bool),ord_less_eq(fun(X5569,bool)),hAPP(fun(X5568,bool),fun(X5569,bool),hAPP(fun(X5568,X5569),fun(fun(X5568,bool),fun(X5569,bool)),image(X5568,X5569),X5571),X5572)),X5570))
      | ~ hBOOL(hAPP(fun(X5569,bool),bool,finite_finite_1(X5569),X5570))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X5568,bool),nat,finite_card(X5568),X5572)),hAPP(fun(X5569,bool),nat,finite_card(X5569),X5570))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_509_card__inj__on__le])]) ).

fof(i_0_1721,plain,
    ! [X4370,X4371,X4372,X4373,X4374,X4375] :
      ( ~ hBOOL(hAPP(fun(fun(X4370,X4371),bool),bool,hAPP(fun(X4370,X4371),fun(fun(fun(X4370,X4371),bool),bool),member(fun(X4370,X4371)),X4373),hAPP(fun(X4370,fun(X4371,bool)),fun(fun(X4370,X4371),bool),hAPP(fun(X4370,bool),fun(fun(X4370,fun(X4371,bool)),fun(fun(X4370,X4371),bool)),pi(X4370,X4371),X4374),hAPP(fun(X4371,bool),fun(X4370,fun(X4371,bool)),combk(fun(X4371,bool),X4370),X4375))))
      | ~ hBOOL(hAPP(fun(X4370,bool),bool,hAPP(X4370,fun(fun(X4370,bool),bool),member(X4370),X4372),X4374))
      | hBOOL(hAPP(fun(X4371,bool),bool,hAPP(X4371,fun(fun(X4371,bool),bool),member(X4371),hAPP(X4370,X4371,X4373,X4372)),X4375)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_funcset__mem])]) ).

fof(i_0_1722,plain,
    ! [X6391,X6392,X6393,X6394,X6395,X6396] :
      ( ~ hBOOL(hAPP(fun(X6391,bool),bool,hAPP(fun(X6391,X6392),fun(fun(X6391,bool),bool),inj_on(X6391,X6392),hAPP(fun(X6391,X6393),fun(X6391,X6392),hAPP(fun(X6393,X6392),fun(fun(X6391,X6393),fun(X6391,X6392)),comp(X6393,X6392,X6391),X6394),X6395)),X6396))
      | hBOOL(hAPP(fun(X6393,bool),bool,hAPP(fun(X6393,X6392),fun(fun(X6393,bool),bool),inj_on(X6393,X6392),X6394),hAPP(fun(X6391,bool),fun(X6393,bool),hAPP(fun(X6391,X6393),fun(fun(X6391,bool),fun(X6393,bool)),image(X6391,X6393),X6395),X6396))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_722_inj__on__imageI])]) ).

cnf(i_0_1723,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1208]) ).

fof(i_0_1724,plain,
    ! [X4456,X4457,X4458,X4459,X4460] :
      ( ~ hBOOL(hAPP(fun(X4457,bool),bool,hAPP(fun(X4457,bool),fun(fun(X4457,bool),bool),ord_less_eq(fun(X4457,bool)),X4459),X4460))
      | hBOOL(hAPP(fun(fun(X4457,X4456),bool),bool,hAPP(fun(fun(X4457,X4456),bool),fun(fun(fun(X4457,X4456),bool),bool),ord_less_eq(fun(fun(X4457,X4456),bool)),hAPP(fun(X4457,fun(X4456,bool)),fun(fun(X4457,X4456),bool),hAPP(fun(X4457,bool),fun(fun(X4457,fun(X4456,bool)),fun(fun(X4457,X4456),bool)),pi(X4457,X4456),X4460),X4458)),hAPP(fun(X4457,fun(X4456,bool)),fun(fun(X4457,X4456),bool),hAPP(fun(X4457,bool),fun(fun(X4457,fun(X4456,bool)),fun(fun(X4457,X4456),bool)),pi(X4457,X4456),X4459),X4458))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_160_Pi__anti__mono])]) ).

fof(i_0_1725,plain,
    ! [X6397,X6398,X6399,X6400,X6401,X6402] :
      ( ~ hBOOL(hAPP(fun(X6398,bool),bool,hAPP(fun(X6398,X6399),fun(fun(X6398,bool),bool),inj_on(X6398,X6399),X6401),X6402))
      | ~ hBOOL(hAPP(fun(X6399,bool),bool,hAPP(fun(X6399,X6397),fun(fun(X6399,bool),bool),inj_on(X6399,X6397),X6400),hAPP(fun(X6398,bool),fun(X6399,bool),hAPP(fun(X6398,X6399),fun(fun(X6398,bool),fun(X6399,bool)),image(X6398,X6399),X6401),X6402)))
      | hBOOL(hAPP(fun(X6398,bool),bool,hAPP(fun(X6398,X6397),fun(fun(X6398,bool),bool),inj_on(X6398,X6397),hAPP(fun(X6398,X6399),fun(X6398,X6397),hAPP(fun(X6399,X6397),fun(fun(X6398,X6399),fun(X6398,X6397)),comp(X6399,X6397,X6398),X6400),X6401)),X6402)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_723_comp__inj__on])]) ).

cnf(i_0_1726,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk145_5(X1,X2,X3,X4,X5)),X5))
    | ti(fun(X1,X2),X4) = ti(fun(X1,X2),X3)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,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)),X4),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_1218]) ).

fof(i_0_1727,plain,
    ! [X7360,X7361,X7362,X7363,X7364] :
      ( ~ comm_monoid_add(X7360)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7363),X7364))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7364),X7362))
      | hAPP(X7360,X7360,hAPP(X7360,fun(X7360,X7360),plus_plus(X7360),hAPP(fun(nat,bool),X7360,hAPP(fun(nat,X7360),fun(fun(nat,bool),X7360),big_co1399186613setsum(nat,X7360),X7361),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7363),X7364))),hAPP(fun(nat,bool),X7360,hAPP(fun(nat,X7360),fun(fun(nat,bool),X7360),big_co1399186613setsum(nat,X7360),X7361),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7364),X7362))) = hAPP(fun(nat,bool),X7360,hAPP(fun(nat,X7360),fun(fun(nat,bool),X7360),big_co1399186613setsum(nat,X7360),X7361),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7363),X7362)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_955_setsum__add__nat__ivl])])]) ).

fof(i_0_1728,plain,
    ! [X6654,X6655,X6656,X6657,X6658] :
      ( ( hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less_eq(X6654),X6657),X6655))
        | ~ hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less_eq(X6654),X6655),X6656))
        | ~ hBOOL(hAPP(fun(X6654,bool),bool,hAPP(fun(X6654,bool),fun(fun(X6654,bool),bool),ord_less_eq(fun(X6654,bool)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastAtMost(X6654),X6655),X6656)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastLessThan(X6654),X6657),X6658)))
        | ~ dense_linorder(X6654) )
      & ( hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less(X6654),X6656),X6658))
        | ~ hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less_eq(X6654),X6655),X6656))
        | ~ hBOOL(hAPP(fun(X6654,bool),bool,hAPP(fun(X6654,bool),fun(fun(X6654,bool),bool),ord_less_eq(fun(X6654,bool)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastAtMost(X6654),X6655),X6656)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastLessThan(X6654),X6657),X6658)))
        | ~ dense_linorder(X6654) )
      & ( hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less_eq(X6654),X6655),X6656))
        | hBOOL(hAPP(fun(X6654,bool),bool,hAPP(fun(X6654,bool),fun(fun(X6654,bool),bool),ord_less_eq(fun(X6654,bool)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastAtMost(X6654),X6655),X6656)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastLessThan(X6654),X6657),X6658)))
        | ~ dense_linorder(X6654) )
      & ( ~ hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less_eq(X6654),X6657),X6655))
        | ~ hBOOL(hAPP(X6654,bool,hAPP(X6654,fun(X6654,bool),ord_less(X6654),X6656),X6658))
        | hBOOL(hAPP(fun(X6654,bool),bool,hAPP(fun(X6654,bool),fun(fun(X6654,bool),bool),ord_less_eq(fun(X6654,bool)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastAtMost(X6654),X6655),X6656)),hAPP(X6654,fun(X6654,bool),hAPP(X6654,fun(X6654,fun(X6654,bool)),ord_atLeastLessThan(X6654),X6657),X6658)))
        | ~ dense_linorder(X6654) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_770_atLeastAtMost__subseteq__atLeastLessThan__iff])])])]) ).

fof(i_0_1729,plain,
    ! [X5725,X5726,X5727,X5728,X5729] :
      ( ( hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less_eq(X5725),X5728),X5726))
        | ~ hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less(X5725),X5726),X5727))
        | ~ hBOOL(hAPP(fun(X5725,bool),bool,hAPP(fun(X5725,bool),fun(fun(X5725,bool),bool),ord_less_eq(fun(X5725,bool)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_gr676655987ssThan(X5725),X5726),X5727)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_atLeastLessThan(X5725),X5728),X5729)))
        | ~ dense_linorder(X5725) )
      & ( hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less_eq(X5725),X5727),X5729))
        | ~ hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less(X5725),X5726),X5727))
        | ~ hBOOL(hAPP(fun(X5725,bool),bool,hAPP(fun(X5725,bool),fun(fun(X5725,bool),bool),ord_less_eq(fun(X5725,bool)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_gr676655987ssThan(X5725),X5726),X5727)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_atLeastLessThan(X5725),X5728),X5729)))
        | ~ dense_linorder(X5725) )
      & ( hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less(X5725),X5726),X5727))
        | hBOOL(hAPP(fun(X5725,bool),bool,hAPP(fun(X5725,bool),fun(fun(X5725,bool),bool),ord_less_eq(fun(X5725,bool)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_gr676655987ssThan(X5725),X5726),X5727)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_atLeastLessThan(X5725),X5728),X5729)))
        | ~ dense_linorder(X5725) )
      & ( ~ hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less_eq(X5725),X5728),X5726))
        | ~ hBOOL(hAPP(X5725,bool,hAPP(X5725,fun(X5725,bool),ord_less_eq(X5725),X5727),X5729))
        | hBOOL(hAPP(fun(X5725,bool),bool,hAPP(fun(X5725,bool),fun(fun(X5725,bool),bool),ord_less_eq(fun(X5725,bool)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_gr676655987ssThan(X5725),X5726),X5727)),hAPP(X5725,fun(X5725,bool),hAPP(X5725,fun(X5725,fun(X5725,bool)),ord_atLeastLessThan(X5725),X5728),X5729)))
        | ~ dense_linorder(X5725) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_545_greaterThanLessThan__subseteq__atLeastLessThan__iff])])])]) ).

fof(i_0_1730,plain,
    ! [X6607,X6608,X6609,X6610,X6611] :
      ( ( hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less_eq(X6607),X6610),X6608))
        | ~ hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less(X6607),X6608),X6609))
        | ~ hBOOL(hAPP(fun(X6607,bool),bool,hAPP(fun(X6607,bool),fun(fun(X6607,bool),bool),ord_less_eq(fun(X6607,bool)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_gr676655987ssThan(X6607),X6608),X6609)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_atLeastAtMost(X6607),X6610),X6611)))
        | ~ dense_linorder(X6607) )
      & ( hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less_eq(X6607),X6609),X6611))
        | ~ hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less(X6607),X6608),X6609))
        | ~ hBOOL(hAPP(fun(X6607,bool),bool,hAPP(fun(X6607,bool),fun(fun(X6607,bool),bool),ord_less_eq(fun(X6607,bool)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_gr676655987ssThan(X6607),X6608),X6609)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_atLeastAtMost(X6607),X6610),X6611)))
        | ~ dense_linorder(X6607) )
      & ( hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less(X6607),X6608),X6609))
        | hBOOL(hAPP(fun(X6607,bool),bool,hAPP(fun(X6607,bool),fun(fun(X6607,bool),bool),ord_less_eq(fun(X6607,bool)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_gr676655987ssThan(X6607),X6608),X6609)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_atLeastAtMost(X6607),X6610),X6611)))
        | ~ dense_linorder(X6607) )
      & ( ~ hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less_eq(X6607),X6610),X6608))
        | ~ hBOOL(hAPP(X6607,bool,hAPP(X6607,fun(X6607,bool),ord_less_eq(X6607),X6609),X6611))
        | hBOOL(hAPP(fun(X6607,bool),bool,hAPP(fun(X6607,bool),fun(fun(X6607,bool),bool),ord_less_eq(fun(X6607,bool)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_gr676655987ssThan(X6607),X6608),X6609)),hAPP(X6607,fun(X6607,bool),hAPP(X6607,fun(X6607,fun(X6607,bool)),ord_atLeastAtMost(X6607),X6610),X6611)))
        | ~ dense_linorder(X6607) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_759_greaterThanLessThan__subseteq__atLeastAtMost__iff])])])]) ).

fof(i_0_1731,plain,
    ! [X5720,X5721,X5722,X5723,X5724] :
      ( ( hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less_eq(X5720),X5723),X5721))
        | ~ hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less(X5720),X5721),X5722))
        | ~ hBOOL(hAPP(fun(X5720,bool),bool,hAPP(fun(X5720,bool),fun(fun(X5720,bool),bool),ord_less_eq(fun(X5720,bool)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_gr1471790799AtMost(X5720),X5721),X5722)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_atLeastLessThan(X5720),X5723),X5724)))
        | ~ dense_linorder(X5720) )
      & ( hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less(X5720),X5722),X5724))
        | ~ hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less(X5720),X5721),X5722))
        | ~ hBOOL(hAPP(fun(X5720,bool),bool,hAPP(fun(X5720,bool),fun(fun(X5720,bool),bool),ord_less_eq(fun(X5720,bool)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_gr1471790799AtMost(X5720),X5721),X5722)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_atLeastLessThan(X5720),X5723),X5724)))
        | ~ dense_linorder(X5720) )
      & ( hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less(X5720),X5721),X5722))
        | hBOOL(hAPP(fun(X5720,bool),bool,hAPP(fun(X5720,bool),fun(fun(X5720,bool),bool),ord_less_eq(fun(X5720,bool)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_gr1471790799AtMost(X5720),X5721),X5722)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_atLeastLessThan(X5720),X5723),X5724)))
        | ~ dense_linorder(X5720) )
      & ( ~ hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less_eq(X5720),X5723),X5721))
        | ~ hBOOL(hAPP(X5720,bool,hAPP(X5720,fun(X5720,bool),ord_less(X5720),X5722),X5724))
        | hBOOL(hAPP(fun(X5720,bool),bool,hAPP(fun(X5720,bool),fun(fun(X5720,bool),bool),ord_less_eq(fun(X5720,bool)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_gr1471790799AtMost(X5720),X5721),X5722)),hAPP(X5720,fun(X5720,bool),hAPP(X5720,fun(X5720,fun(X5720,bool)),ord_atLeastLessThan(X5720),X5723),X5724)))
        | ~ dense_linorder(X5720) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_544_greaterThanAtMost__subseteq__atLeastLessThan__iff])])])]) ).

fof(i_0_1732,plain,
    ! [X6612,X6613,X6614,X6615,X6616] :
      ( ( hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less_eq(X6612),X6615),X6613))
        | ~ hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less(X6612),X6613),X6614))
        | ~ hBOOL(hAPP(fun(X6612,bool),bool,hAPP(fun(X6612,bool),fun(fun(X6612,bool),bool),ord_less_eq(fun(X6612,bool)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_gr1471790799AtMost(X6612),X6613),X6614)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_atLeastAtMost(X6612),X6615),X6616)))
        | ~ dense_linorder(X6612) )
      & ( hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less_eq(X6612),X6614),X6616))
        | ~ hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less(X6612),X6613),X6614))
        | ~ hBOOL(hAPP(fun(X6612,bool),bool,hAPP(fun(X6612,bool),fun(fun(X6612,bool),bool),ord_less_eq(fun(X6612,bool)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_gr1471790799AtMost(X6612),X6613),X6614)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_atLeastAtMost(X6612),X6615),X6616)))
        | ~ dense_linorder(X6612) )
      & ( hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less(X6612),X6613),X6614))
        | hBOOL(hAPP(fun(X6612,bool),bool,hAPP(fun(X6612,bool),fun(fun(X6612,bool),bool),ord_less_eq(fun(X6612,bool)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_gr1471790799AtMost(X6612),X6613),X6614)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_atLeastAtMost(X6612),X6615),X6616)))
        | ~ dense_linorder(X6612) )
      & ( ~ hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less_eq(X6612),X6615),X6613))
        | ~ hBOOL(hAPP(X6612,bool,hAPP(X6612,fun(X6612,bool),ord_less_eq(X6612),X6614),X6616))
        | hBOOL(hAPP(fun(X6612,bool),bool,hAPP(fun(X6612,bool),fun(fun(X6612,bool),bool),ord_less_eq(fun(X6612,bool)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_gr1471790799AtMost(X6612),X6613),X6614)),hAPP(X6612,fun(X6612,bool),hAPP(X6612,fun(X6612,fun(X6612,bool)),ord_atLeastAtMost(X6612),X6615),X6616)))
        | ~ dense_linorder(X6612) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_760_greaterThanAtMost__subseteq__atLeastAtMost__iff])])])]) ).

fof(i_0_1733,plain,
    ! [X6659,X6660,X6661,X6662,X6663] :
      ( ( hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less_eq(X6659),X6662),X6660))
        | ~ hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less(X6659),X6660),X6661))
        | ~ hBOOL(hAPP(fun(X6659,bool),bool,hAPP(fun(X6659,bool),fun(fun(X6659,bool),bool),ord_less_eq(fun(X6659,bool)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastLessThan(X6659),X6660),X6661)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastAtMost(X6659),X6662),X6663)))
        | ~ dense_linorder(X6659) )
      & ( hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less_eq(X6659),X6661),X6663))
        | ~ hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less(X6659),X6660),X6661))
        | ~ hBOOL(hAPP(fun(X6659,bool),bool,hAPP(fun(X6659,bool),fun(fun(X6659,bool),bool),ord_less_eq(fun(X6659,bool)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastLessThan(X6659),X6660),X6661)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastAtMost(X6659),X6662),X6663)))
        | ~ dense_linorder(X6659) )
      & ( hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less(X6659),X6660),X6661))
        | hBOOL(hAPP(fun(X6659,bool),bool,hAPP(fun(X6659,bool),fun(fun(X6659,bool),bool),ord_less_eq(fun(X6659,bool)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastLessThan(X6659),X6660),X6661)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastAtMost(X6659),X6662),X6663)))
        | ~ dense_linorder(X6659) )
      & ( ~ hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less_eq(X6659),X6662),X6660))
        | ~ hBOOL(hAPP(X6659,bool,hAPP(X6659,fun(X6659,bool),ord_less_eq(X6659),X6661),X6663))
        | hBOOL(hAPP(fun(X6659,bool),bool,hAPP(fun(X6659,bool),fun(fun(X6659,bool),bool),ord_less_eq(fun(X6659,bool)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastLessThan(X6659),X6660),X6661)),hAPP(X6659,fun(X6659,bool),hAPP(X6659,fun(X6659,fun(X6659,bool)),ord_atLeastAtMost(X6659),X6662),X6663)))
        | ~ dense_linorder(X6659) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_771_atLeastLessThan__subseteq__atLeastAtMost__iff])])])]) ).

fof(i_0_1734,plain,
    ! [X6619,X6620,X6621,X6622,X6623] :
      ( ( hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6622),X6620))
        | ~ hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6620),X6621))
        | ~ hBOOL(hAPP(fun(X6619,bool),bool,hAPP(fun(X6619,bool),fun(fun(X6619,bool),bool),ord_less_eq(fun(X6619,bool)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6620),X6621)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6622),X6623)))
        | ~ order(X6619) )
      & ( hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6621),X6623))
        | ~ hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6620),X6621))
        | ~ hBOOL(hAPP(fun(X6619,bool),bool,hAPP(fun(X6619,bool),fun(fun(X6619,bool),bool),ord_less_eq(fun(X6619,bool)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6620),X6621)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6622),X6623)))
        | ~ order(X6619) )
      & ( hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6620),X6621))
        | hBOOL(hAPP(fun(X6619,bool),bool,hAPP(fun(X6619,bool),fun(fun(X6619,bool),bool),ord_less_eq(fun(X6619,bool)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6620),X6621)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6622),X6623)))
        | ~ order(X6619) )
      & ( ~ hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6622),X6620))
        | ~ hBOOL(hAPP(X6619,bool,hAPP(X6619,fun(X6619,bool),ord_less_eq(X6619),X6621),X6623))
        | hBOOL(hAPP(fun(X6619,bool),bool,hAPP(fun(X6619,bool),fun(fun(X6619,bool),bool),ord_less_eq(fun(X6619,bool)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6620),X6621)),hAPP(X6619,fun(X6619,bool),hAPP(X6619,fun(X6619,fun(X6619,bool)),ord_atLeastAtMost(X6619),X6622),X6623)))
        | ~ order(X6619) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1219])])])]) ).

cnf(i_0_1735,plain,
    ( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

cnf(i_0_1736,plain,
    ( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ti(arrow_2142409994le_alt,X3) != ti(arrow_2142409994le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

cnf(i_0_1737,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1207]) ).

cnf(i_0_1738,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1207]) ).

fof(i_0_1739,plain,
    ! [X6237,X6238,X6239] :
      ( ~ linordered_ring(X6237)
      | hBOOL(hAPP(X6237,bool,hAPP(X6237,fun(X6237,bool),ord_less_eq(X6237),zero_zero(X6237)),hAPP(X6237,X6237,hAPP(X6237,fun(X6237,X6237),plus_plus(X6237),hAPP(X6237,X6237,hAPP(X6237,fun(X6237,X6237),times_times(X6237),X6238),X6238)),hAPP(X6237,X6237,hAPP(X6237,fun(X6237,X6237),times_times(X6237),X6239),X6239)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_685_sum__squares__ge__zero])])]) ).

fof(i_0_1740,plain,
    ! [X6575,X6576,X6577,X6578,X6579] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X6575,nat,X6577,X6578)),hAPP(X6575,nat,X6577,X6579)))
      | hBOOL(hAPP(fun(product_prod(X6575,X6575),bool),bool,hAPP(product_prod(X6575,X6575),fun(fun(product_prod(X6575,X6575),bool),bool),member(product_prod(X6575,X6575)),hAPP(X6575,product_prod(X6575,X6575),hAPP(X6575,fun(X6575,product_prod(X6575,X6575)),product_Pair(X6575,X6575),X6578),X6579)),hAPP(fun(product_prod(X6575,X6575),bool),fun(product_prod(X6575,X6575),bool),hAPP(fun(X6575,nat),fun(fun(product_prod(X6575,X6575),bool),fun(product_prod(X6575,X6575),bool)),mlex_prod(X6575),X6577),X6576))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_754_mlex__less])]) ).

cnf(i_0_1741,plain,
    ( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

cnf(i_0_1742,plain,
    ( ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

fof(i_0_1743,plain,
    ! [X5497,X5498,X5499,X5500,X5501] :
      ( ( hBOOL(hAPP(X5497,bool,hAPP(X5497,fun(X5497,bool),ord_less_eq(X5497),X5500),X5498))
        | hBOOL(hAPP(X5497,bool,hAPP(X5497,fun(X5497,bool),ord_less_eq(X5497),X5499),X5498))
        | ~ hBOOL(hAPP(fun(X5497,bool),bool,hAPP(fun(X5497,bool),fun(fun(X5497,bool),bool),ord_less_eq(fun(X5497,bool)),hAPP(X5497,fun(X5497,bool),hAPP(X5497,fun(X5497,fun(X5497,bool)),ord_atLeastLessThan(X5497),X5498),X5499)),hAPP(X5497,fun(X5497,bool),hAPP(X5497,fun(X5497,fun(X5497,bool)),ord_atLeastLessThan(X5497),X5500),X5501)))
        | ~ linorder(X5497) )
      & ( hBOOL(hAPP(X5497,bool,hAPP(X5497,fun(X5497,bool),ord_less_eq(X5497),X5499),X5501))
        | hBOOL(hAPP(X5497,bool,hAPP(X5497,fun(X5497,bool),ord_less_eq(X5497),X5499),X5498))
        | ~ hBOOL(hAPP(fun(X5497,bool),bool,hAPP(fun(X5497,bool),fun(fun(X5497,bool),bool),ord_less_eq(fun(X5497,bool)),hAPP(X5497,fun(X5497,bool),hAPP(X5497,fun(X5497,fun(X5497,bool)),ord_atLeastLessThan(X5497),X5498),X5499)),hAPP(X5497,fun(X5497,bool),hAPP(X5497,fun(X5497,fun(X5497,bool)),ord_atLeastLessThan(X5497),X5500),X5501)))
        | ~ linorder(X5497) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_491_atLeastLessThan__subset__iff])])])]) ).

fof(i_0_1744,plain,
    ! [X5522,X5523,X5524,X5525] :
      ( ~ hBOOL(hAPP(fun(X5523,bool),bool,finite_finite_1(X5523),X5525))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X5522,bool),nat,finite_card(X5522),hAPP(fun(X5523,bool),fun(X5522,bool),hAPP(fun(X5523,X5522),fun(fun(X5523,bool),fun(X5522,bool)),image(X5523,X5522),X5524),X5525))),hAPP(fun(X5523,bool),nat,finite_card(X5523),X5525))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_498_card__image__le])]) ).

fof(i_0_1745,plain,
    ! [X6544,X6545,X6546,X6547] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(X6544,X6544),bool),bool,hAPP(product_prod(X6544,X6544),fun(fun(product_prod(X6544,X6544),bool),bool),member(product_prod(X6544,X6544)),hAPP(X6544,product_prod(X6544,X6544),hAPP(X6544,fun(X6544,product_prod(X6544,X6544)),product_Pair(X6544,X6544),X6545),X6546)),hAPP(fun(X6544,nat),fun(product_prod(X6544,X6544),bool),measure(X6544),X6547)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X6544,nat,X6547,X6545)),hAPP(X6544,nat,X6547,X6546))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X6544,nat,X6547,X6545)),hAPP(X6544,nat,X6547,X6546)))
        | hBOOL(hAPP(fun(product_prod(X6544,X6544),bool),bool,hAPP(product_prod(X6544,X6544),fun(fun(product_prod(X6544,X6544),bool),bool),member(product_prod(X6544,X6544)),hAPP(X6544,product_prod(X6544,X6544),hAPP(X6544,fun(X6544,product_prod(X6544,X6544)),product_Pair(X6544,X6544),X6545),X6546)),hAPP(fun(X6544,nat),fun(product_prod(X6544,X6544),bool),measure(X6544),X6547))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_748_in__measure])]) ).

cnf(i_0_1746,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_1220]) ).

fof(i_0_1747,plain,
    ! [X6725,X6726,X6727,X6728,X6729] :
      ( ~ hBOOL(hAPP(fun(X6725,bool),bool,hAPP(fun(X6725,bool),fun(fun(X6725,bool),bool),ord_less_eq(fun(X6725,bool)),X6728),X6729))
      | ~ hBOOL(hAPP(fun(X6725,bool),bool,hAPP(fun(X6725,bool),fun(fun(X6725,bool),bool),ord_less_eq(fun(X6725,bool)),X6726),X6727))
      | hBOOL(hAPP(fun(X6725,bool),bool,hAPP(fun(X6725,bool),fun(fun(X6725,bool),bool),ord_less_eq(fun(X6725,bool)),hAPP(fun(X6725,bool),fun(X6725,bool),hAPP(fun(X6725,bool),fun(fun(X6725,bool),fun(X6725,bool)),semilattice_sup_sup(fun(X6725,bool)),X6728),X6726)),hAPP(fun(X6725,bool),fun(X6725,bool),hAPP(fun(X6725,bool),fun(fun(X6725,bool),fun(X6725,bool)),semilattice_sup_sup(fun(X6725,bool)),X6729),X6727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_788_Un__mono])]) ).

fof(i_0_1748,plain,
    ! [X7194,X7195,X7196,X7197,X7198] :
      ( ~ hBOOL(hAPP(fun(X7194,bool),bool,hAPP(fun(X7194,bool),fun(fun(X7194,bool),bool),ord_less_eq(fun(X7194,bool)),X7197),X7198))
      | ~ hBOOL(hAPP(fun(X7194,bool),bool,hAPP(fun(X7194,bool),fun(fun(X7194,bool),bool),ord_less_eq(fun(X7194,bool)),X7195),X7196))
      | hBOOL(hAPP(fun(X7194,bool),bool,hAPP(fun(X7194,bool),fun(fun(X7194,bool),bool),ord_less_eq(fun(X7194,bool)),hAPP(fun(X7194,bool),fun(X7194,bool),hAPP(fun(X7194,bool),fun(fun(X7194,bool),fun(X7194,bool)),semilattice_inf_inf(fun(X7194,bool)),X7197),X7195)),hAPP(fun(X7194,bool),fun(X7194,bool),hAPP(fun(X7194,bool),fun(fun(X7194,bool),fun(X7194,bool)),semilattice_inf_inf(fun(X7194,bool)),X7198),X7196))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_909_Int__mono])]) ).

fof(i_0_1749,plain,
    ! [X7437,X7438,X7439,X7440,X7441,X7442] :
      ( ~ hBOOL(hAPP(X7437,bool,hAPP(X7438,fun(X7437,bool),X7440,X7441),X7442))
      | ~ hBOOL(hAPP(X7437,bool,hAPP(X7438,fun(X7437,bool),X7439,X7441),X7442))
      | hBOOL(hAPP(X7437,bool,hAPP(X7438,fun(X7437,bool),hAPP(fun(X7438,fun(X7437,bool)),fun(X7438,fun(X7437,bool)),hAPP(fun(X7438,fun(X7437,bool)),fun(fun(X7438,fun(X7437,bool)),fun(X7438,fun(X7437,bool))),semilattice_inf_inf(fun(X7438,fun(X7437,bool))),X7440),X7439),X7441),X7442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_973_inf2I])]) ).

fof(i_0_1750,plain,
    ! [X4359,X4360,X4361,X4362,X4363,X4364] :
      ( ~ hBOOL(hAPP(fun(fun(X4359,X4360),bool),bool,hAPP(fun(X4359,X4360),fun(fun(fun(X4359,X4360),bool),bool),member(fun(X4359,X4360)),X4362),hAPP(fun(X4359,fun(X4360,bool)),fun(fun(X4359,X4360),bool),hAPP(fun(X4359,bool),fun(fun(X4359,fun(X4360,bool)),fun(fun(X4359,X4360),bool)),pi(X4359,X4360),X4363),X4364)))
      | ~ hBOOL(hAPP(fun(X4359,bool),bool,hAPP(X4359,fun(fun(X4359,bool),bool),member(X4359),X4361),X4363))
      | hBOOL(hAPP(fun(X4360,bool),bool,hAPP(X4360,fun(fun(X4360,bool),bool),member(X4360),hAPP(X4359,X4360,X4362,X4361)),hAPP(X4359,fun(X4360,bool),X4364,X4361))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_Pi__mem])]) ).

fof(i_0_1751,plain,
    ! [X4166,X4167,X4168,X4169,X4170,X4171] :
      ( ~ hBOOL(hAPP(fun(fun(X4166,X4167),bool),bool,hAPP(fun(X4166,X4167),fun(fun(fun(X4166,X4167),bool),bool),member(fun(X4166,X4167)),X4169),hAPP(fun(X4166,fun(X4167,bool)),fun(fun(X4166,X4167),bool),hAPP(fun(X4166,bool),fun(fun(X4166,fun(X4167,bool)),fun(fun(X4166,X4167),bool)),pi(X4166,X4167),X4170),X4171)))
      | hBOOL(hAPP(fun(X4167,bool),bool,hAPP(X4167,fun(fun(X4167,bool),bool),member(X4167),hAPP(X4166,X4167,X4169,X4168)),hAPP(X4166,fun(X4167,bool),X4171,X4168)))
      | ~ hBOOL(hAPP(fun(X4166,bool),bool,hAPP(X4166,fun(fun(X4166,bool),bool),member(X4166),X4168),X4170)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1221])]) ).

cnf(i_0_1752,plain,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,esk145_5(X1,X2,X4,X3,X5)) != hAPP(X1,X2,X4,esk145_5(X1,X2,X4,X3,X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_1218]) ).

fof(i_0_1753,plain,
    ! [X5485,X5486,X5487,X5488,X5489] :
      ( ~ hBOOL(hAPP(fun(X5485,bool),bool,hAPP(fun(X5485,X5486),fun(fun(X5485,bool),bool),inj_on(X5485,X5486),X5488),X5489))
      | ~ hBOOL(hAPP(fun(X5485,bool),bool,hAPP(fun(X5485,bool),fun(fun(X5485,bool),bool),ord_less(fun(X5485,bool)),X5487),X5489))
      | hBOOL(hAPP(fun(X5486,bool),bool,hAPP(fun(X5486,bool),fun(fun(X5486,bool),bool),ord_less(fun(X5486,bool)),hAPP(fun(X5485,bool),fun(X5486,bool),hAPP(fun(X5485,X5486),fun(fun(X5485,bool),fun(X5486,bool)),image(X5485,X5486),X5488),X5487)),hAPP(fun(X5485,bool),fun(X5486,bool),hAPP(fun(X5485,X5486),fun(fun(X5485,bool),fun(X5486,bool)),image(X5485,X5486),X5488),X5489))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_488_inj__on__strict__subset])]) ).

fof(i_0_1754,plain,
    ! [X4929,X4930] :
      ( ( ~ hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),collect(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),hAPP(fun(bool,bool),fun(fun(X4929,bool),fun(X4929,bool)),combb(bool,bool,X4929),fNot),X4930))))
        | hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),top_top(fun(X4929,bool))))
        | ~ hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),collect(X4929),X4930))) )
      & ( ~ hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),top_top(fun(X4929,bool))))
        | hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),collect(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),hAPP(fun(bool,bool),fun(fun(X4929,bool),fun(X4929,bool)),combb(bool,bool,X4929),fNot),X4930))))
        | ~ hBOOL(hAPP(fun(X4929,bool),bool,finite_finite_1(X4929),hAPP(fun(X4929,bool),fun(X4929,bool),collect(X4929),X4930))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_finite__Collect__not])])]) ).

cnf(i_0_1755,plain,
    ( hAPP(fun(X1,bool),fun(X6,bool),hAPP(fun(X1,X6),fun(fun(X1,bool),fun(X6,bool)),image(X1,X6),hAPP(fun(X1,X2),fun(X1,X6),hAPP(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6)),hAPP(fun(X1,bool),fun(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6))),compose(X1,X2,X6),X4),X7),X3)),X4) = ti(fun(X6,bool),X8)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X5)
    | hAPP(fun(X2,bool),fun(X6,bool),hAPP(fun(X2,X6),fun(fun(X2,bool),fun(X6,bool)),image(X2,X6),X7),X5) != ti(fun(X6,bool),X8) ),
    inference(split_conjunct,[status(thm)],[i_0_1222]) ).

fof(i_0_1756,plain,
    ! [X6229,X6230,X6231,X6232] :
      ( ~ linord20386208strict(X6229)
      | ~ hBOOL(hAPP(X6229,bool,hAPP(X6229,fun(X6229,bool),ord_less_eq(X6229),hAPP(X6229,X6229,hAPP(X6229,fun(X6229,X6229),times_times(X6229),X6230),X6231)),hAPP(X6229,X6229,hAPP(X6229,fun(X6229,X6229),times_times(X6229),X6232),X6231)))
      | ~ hBOOL(hAPP(X6229,bool,hAPP(X6229,fun(X6229,bool),ord_less(X6229),zero_zero(X6229)),X6231))
      | hBOOL(hAPP(X6229,bool,hAPP(X6229,fun(X6229,bool),ord_less_eq(X6229),X6230),X6232)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_683_mult__right__le__imp__le])])]) ).

fof(i_0_1757,plain,
    ! [X6233,X6234,X6235,X6236] :
      ( ~ linord20386208strict(X6233)
      | ~ hBOOL(hAPP(X6233,bool,hAPP(X6233,fun(X6233,bool),ord_less_eq(X6233),hAPP(X6233,X6233,hAPP(X6233,fun(X6233,X6233),times_times(X6233),X6234),X6235)),hAPP(X6233,X6233,hAPP(X6233,fun(X6233,X6233),times_times(X6233),X6234),X6236)))
      | ~ hBOOL(hAPP(X6233,bool,hAPP(X6233,fun(X6233,bool),ord_less(X6233),zero_zero(X6233)),X6234))
      | hBOOL(hAPP(X6233,bool,hAPP(X6233,fun(X6233,bool),ord_less_eq(X6233),X6235),X6236)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_684_mult__left__le__imp__le])])]) ).

fof(i_0_1758,plain,
    ! [X6185,X6186,X6187,X6188] :
      ( ( ~ hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less_eq(X6185),hAPP(X6185,X6185,hAPP(X6185,fun(X6185,X6185),times_times(X6185),X6188),X6186)),hAPP(X6185,X6185,hAPP(X6185,fun(X6185,X6185),times_times(X6185),X6188),X6187)))
        | hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less_eq(X6185),X6186),X6187))
        | ~ hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less(X6185),zero_zero(X6185)),X6188))
        | ~ linord581940658strict(X6185) )
      & ( ~ hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less_eq(X6185),X6186),X6187))
        | hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less_eq(X6185),hAPP(X6185,X6185,hAPP(X6185,fun(X6185,X6185),times_times(X6185),X6188),X6186)),hAPP(X6185,X6185,hAPP(X6185,fun(X6185,X6185),times_times(X6185),X6188),X6187)))
        | ~ hBOOL(hAPP(X6185,bool,hAPP(X6185,fun(X6185,bool),ord_less(X6185),zero_zero(X6185)),X6188))
        | ~ linord581940658strict(X6185) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_673_mult__le__cancel__left__pos])])])]) ).

fof(i_0_1759,plain,
    ! [X6213,X6214,X6215,X6216] :
      ( ~ linordered_semiring(X6213)
      | ~ hBOOL(hAPP(X6213,bool,hAPP(X6213,fun(X6213,bool),ord_less(X6213),hAPP(X6213,X6213,hAPP(X6213,fun(X6213,X6213),times_times(X6213),X6214),X6215)),hAPP(X6213,X6213,hAPP(X6213,fun(X6213,X6213),times_times(X6213),X6216),X6215)))
      | ~ hBOOL(hAPP(X6213,bool,hAPP(X6213,fun(X6213,bool),ord_less_eq(X6213),zero_zero(X6213)),X6215))
      | hBOOL(hAPP(X6213,bool,hAPP(X6213,fun(X6213,bool),ord_less(X6213),X6214),X6216)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_679_mult__right__less__imp__less])])]) ).

fof(i_0_1760,plain,
    ! [X6217,X6218,X6219,X6220] :
      ( ~ linord20386208strict(X6217)
      | ~ hBOOL(hAPP(X6217,bool,hAPP(X6217,fun(X6217,bool),ord_less(X6217),hAPP(X6217,X6217,hAPP(X6217,fun(X6217,X6217),times_times(X6217),X6218),X6219)),hAPP(X6217,X6217,hAPP(X6217,fun(X6217,X6217),times_times(X6217),X6220),X6219)))
      | ~ hBOOL(hAPP(X6217,bool,hAPP(X6217,fun(X6217,bool),ord_less_eq(X6217),zero_zero(X6217)),X6219))
      | hBOOL(hAPP(X6217,bool,hAPP(X6217,fun(X6217,bool),ord_less(X6217),X6218),X6220)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_680_mult__less__imp__less__right])])]) ).

fof(i_0_1761,plain,
    ! [X6221,X6222,X6223,X6224] :
      ( ~ linordered_semiring(X6221)
      | ~ hBOOL(hAPP(X6221,bool,hAPP(X6221,fun(X6221,bool),ord_less(X6221),hAPP(X6221,X6221,hAPP(X6221,fun(X6221,X6221),times_times(X6221),X6222),X6223)),hAPP(X6221,X6221,hAPP(X6221,fun(X6221,X6221),times_times(X6221),X6222),X6224)))
      | ~ hBOOL(hAPP(X6221,bool,hAPP(X6221,fun(X6221,bool),ord_less_eq(X6221),zero_zero(X6221)),X6222))
      | hBOOL(hAPP(X6221,bool,hAPP(X6221,fun(X6221,bool),ord_less(X6221),X6223),X6224)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_681_mult__left__less__imp__less])])]) ).

fof(i_0_1762,plain,
    ! [X6225,X6226,X6227,X6228] :
      ( ~ linord20386208strict(X6225)
      | ~ hBOOL(hAPP(X6225,bool,hAPP(X6225,fun(X6225,bool),ord_less(X6225),hAPP(X6225,X6225,hAPP(X6225,fun(X6225,X6225),times_times(X6225),X6226),X6227)),hAPP(X6225,X6225,hAPP(X6225,fun(X6225,X6225),times_times(X6225),X6226),X6228)))
      | ~ hBOOL(hAPP(X6225,bool,hAPP(X6225,fun(X6225,bool),ord_less_eq(X6225),zero_zero(X6225)),X6226))
      | hBOOL(hAPP(X6225,bool,hAPP(X6225,fun(X6225,bool),ord_less(X6225),X6227),X6228)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_682_mult__less__imp__less__left])])]) ).

fof(i_0_1763,plain,
    ! [X6074,X6075,X6076,X6077] :
      ( ( ~ hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),hAPP(X6074,X6074,hAPP(X6074,fun(X6074,X6074),times_times(X6074),X6077),X6075)),hAPP(X6074,X6074,hAPP(X6074,fun(X6074,X6074),times_times(X6074),X6077),X6076)))
        | hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),X6075),X6076))
        | ~ hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),zero_zero(X6074)),X6077))
        | ~ linord581940658strict(X6074) )
      & ( ~ hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),X6075),X6076))
        | hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),hAPP(X6074,X6074,hAPP(X6074,fun(X6074,X6074),times_times(X6074),X6077),X6075)),hAPP(X6074,X6074,hAPP(X6074,fun(X6074,X6074),times_times(X6074),X6077),X6076)))
        | ~ hBOOL(hAPP(X6074,bool,hAPP(X6074,fun(X6074,bool),ord_less(X6074),zero_zero(X6074)),X6077))
        | ~ linord581940658strict(X6074) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_639_mult__less__cancel__left__pos])])])]) ).

fof(i_0_1764,plain,
    ! [X6189,X6190,X6191,X6192] :
      ( ( ~ hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less_eq(X6189),hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),X6192),X6190)),hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),X6192),X6191)))
        | hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less_eq(X6189),X6191),X6190))
        | ~ hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less(X6189),X6192),zero_zero(X6189)))
        | ~ linord581940658strict(X6189) )
      & ( ~ hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less_eq(X6189),X6191),X6190))
        | hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less_eq(X6189),hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),X6192),X6190)),hAPP(X6189,X6189,hAPP(X6189,fun(X6189,X6189),times_times(X6189),X6192),X6191)))
        | ~ hBOOL(hAPP(X6189,bool,hAPP(X6189,fun(X6189,bool),ord_less(X6189),X6192),zero_zero(X6189)))
        | ~ linord581940658strict(X6189) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_674_mult__le__cancel__left__neg])])])]) ).

fof(i_0_1765,plain,
    ! [X6093,X6094,X6095,X6096] :
      ( ( ~ hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),hAPP(X6093,X6093,hAPP(X6093,fun(X6093,X6093),times_times(X6093),X6096),X6094)),hAPP(X6093,X6093,hAPP(X6093,fun(X6093,X6093),times_times(X6093),X6096),X6095)))
        | hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),X6095),X6094))
        | ~ hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),X6096),zero_zero(X6093)))
        | ~ linord581940658strict(X6093) )
      & ( ~ hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),X6095),X6094))
        | hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),hAPP(X6093,X6093,hAPP(X6093,fun(X6093,X6093),times_times(X6093),X6096),X6094)),hAPP(X6093,X6093,hAPP(X6093,fun(X6093,X6093),times_times(X6093),X6096),X6095)))
        | ~ hBOOL(hAPP(X6093,bool,hAPP(X6093,fun(X6093,bool),ord_less(X6093),X6096),zero_zero(X6093)))
        | ~ linord581940658strict(X6093) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_645_mult__less__cancel__left__neg])])])]) ).

fof(i_0_1766,plain,
    ! [X6415,X6416,X6417,X6418,X6419,X6420] :
      ( ~ hBOOL(hAPP(fun(X6415,bool),bool,hAPP(fun(X6415,X6416),fun(fun(X6415,bool),bool),inj_on(X6415,X6416),hAPP(fun(X6415,X6417),fun(X6415,X6416),hAPP(fun(X6417,X6416),fun(fun(X6415,X6417),fun(X6415,X6416)),comp(X6417,X6416,X6415),X6418),X6419)),X6420))
      | hBOOL(hAPP(fun(X6415,bool),bool,hAPP(fun(X6415,X6417),fun(fun(X6415,bool),bool),inj_on(X6415,X6417),X6419),X6420)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_726_inj__on__imageI2])]) ).

fof(i_0_1767,plain,
    ! [X5543,X5544,X5545,X5546,X5547] :
      ( ~ hBOOL(hAPP(fun(X5543,bool),bool,hAPP(fun(X5543,bool),fun(fun(X5543,bool),bool),ord_less_eq(fun(X5543,bool)),X5545),hAPP(fun(X5544,bool),fun(X5543,bool),hAPP(fun(X5544,X5543),fun(fun(X5544,bool),fun(X5543,bool)),image(X5544,X5543),X5546),X5547)))
      | hBOOL(hAPP(fun(X5543,bool),bool,hAPP(fun(X5543,X5544),fun(fun(X5543,bool),bool),inj_on(X5543,X5544),hAPP(fun(X5544,X5543),fun(X5543,X5544),hAPP(fun(X5544,bool),fun(fun(X5544,X5543),fun(X5543,X5544)),hilbert_inv_into(X5544,X5543),X5547),X5546)),X5545)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_503_inj__on__inv__into])]) ).

fof(i_0_1768,plain,
    ! [X6048,X6049,X6050,X6051,X6052] :
      ( ~ ordered_semiring(X6048)
      | ~ hBOOL(hAPP(X6048,bool,hAPP(X6048,fun(X6048,bool),ord_less_eq(X6048),X6051),X6052))
      | ~ hBOOL(hAPP(X6048,bool,hAPP(X6048,fun(X6048,bool),ord_less_eq(X6048),X6049),X6050))
      | ~ hBOOL(hAPP(X6048,bool,hAPP(X6048,fun(X6048,bool),ord_less_eq(X6048),zero_zero(X6048)),X6051))
      | ~ hBOOL(hAPP(X6048,bool,hAPP(X6048,fun(X6048,bool),ord_less_eq(X6048),zero_zero(X6048)),X6049))
      | hBOOL(hAPP(X6048,bool,hAPP(X6048,fun(X6048,bool),ord_less_eq(X6048),hAPP(X6048,X6048,hAPP(X6048,fun(X6048,X6048),times_times(X6048),X6051),X6049)),hAPP(X6048,X6048,hAPP(X6048,fun(X6048,X6048),times_times(X6048),X6052),X6050))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_632_mult__mono_H])])]) ).

fof(i_0_1769,plain,
    ! [X6053,X6054,X6055,X6056,X6057] :
      ( ~ ordered_semiring(X6053)
      | ~ hBOOL(hAPP(X6053,bool,hAPP(X6053,fun(X6053,bool),ord_less_eq(X6053),X6056),X6057))
      | ~ hBOOL(hAPP(X6053,bool,hAPP(X6053,fun(X6053,bool),ord_less_eq(X6053),X6054),X6055))
      | ~ hBOOL(hAPP(X6053,bool,hAPP(X6053,fun(X6053,bool),ord_less_eq(X6053),zero_zero(X6053)),X6057))
      | ~ hBOOL(hAPP(X6053,bool,hAPP(X6053,fun(X6053,bool),ord_less_eq(X6053),zero_zero(X6053)),X6054))
      | hBOOL(hAPP(X6053,bool,hAPP(X6053,fun(X6053,bool),ord_less_eq(X6053),hAPP(X6053,X6053,hAPP(X6053,fun(X6053,X6053),times_times(X6053),X6056),X6054)),hAPP(X6053,X6053,hAPP(X6053,fun(X6053,X6053),times_times(X6053),X6057),X6055))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_633_mult__mono])])]) ).

fof(i_0_1770,plain,
    ! [X6203,X6204,X6205,X6206,X6207] :
      ( ~ linord20386208strict(X6203)
      | ~ hBOOL(hAPP(X6203,bool,hAPP(X6203,fun(X6203,bool),ord_less(X6203),X6206),X6207))
      | ~ hBOOL(hAPP(X6203,bool,hAPP(X6203,fun(X6203,bool),ord_less_eq(X6203),X6204),X6205))
      | ~ hBOOL(hAPP(X6203,bool,hAPP(X6203,fun(X6203,bool),ord_less_eq(X6203),zero_zero(X6203)),X6206))
      | ~ hBOOL(hAPP(X6203,bool,hAPP(X6203,fun(X6203,bool),ord_less(X6203),zero_zero(X6203)),X6204))
      | hBOOL(hAPP(X6203,bool,hAPP(X6203,fun(X6203,bool),ord_less(X6203),hAPP(X6203,X6203,hAPP(X6203,fun(X6203,X6203),times_times(X6203),X6206),X6204)),hAPP(X6203,X6203,hAPP(X6203,fun(X6203,X6203),times_times(X6203),X6207),X6205))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_677_mult__less__le__imp__less])])]) ).

fof(i_0_1771,plain,
    ! [X6208,X6209,X6210,X6211,X6212] :
      ( ~ linord20386208strict(X6208)
      | ~ hBOOL(hAPP(X6208,bool,hAPP(X6208,fun(X6208,bool),ord_less_eq(X6208),X6211),X6212))
      | ~ hBOOL(hAPP(X6208,bool,hAPP(X6208,fun(X6208,bool),ord_less(X6208),X6209),X6210))
      | ~ hBOOL(hAPP(X6208,bool,hAPP(X6208,fun(X6208,bool),ord_less(X6208),zero_zero(X6208)),X6211))
      | ~ hBOOL(hAPP(X6208,bool,hAPP(X6208,fun(X6208,bool),ord_less_eq(X6208),zero_zero(X6208)),X6209))
      | hBOOL(hAPP(X6208,bool,hAPP(X6208,fun(X6208,bool),ord_less(X6208),hAPP(X6208,X6208,hAPP(X6208,fun(X6208,X6208),times_times(X6208),X6211),X6209)),hAPP(X6208,X6208,hAPP(X6208,fun(X6208,X6208),times_times(X6208),X6212),X6210))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_678_mult__le__less__imp__less])])]) ).

fof(i_0_1772,plain,
    ! [X6198,X6199,X6200,X6201,X6202] :
      ( ~ linord20386208strict(X6198)
      | ~ hBOOL(hAPP(X6198,bool,hAPP(X6198,fun(X6198,bool),ord_less(X6198),X6201),X6202))
      | ~ hBOOL(hAPP(X6198,bool,hAPP(X6198,fun(X6198,bool),ord_less(X6198),X6199),X6200))
      | ~ hBOOL(hAPP(X6198,bool,hAPP(X6198,fun(X6198,bool),ord_less_eq(X6198),zero_zero(X6198)),X6201))
      | ~ hBOOL(hAPP(X6198,bool,hAPP(X6198,fun(X6198,bool),ord_less_eq(X6198),zero_zero(X6198)),X6199))
      | hBOOL(hAPP(X6198,bool,hAPP(X6198,fun(X6198,bool),ord_less(X6198),hAPP(X6198,X6198,hAPP(X6198,fun(X6198,X6198),times_times(X6198),X6201),X6199)),hAPP(X6198,X6198,hAPP(X6198,fun(X6198,X6198),times_times(X6198),X6202),X6200))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_676_mult__strict__mono_H])])]) ).

fof(i_0_1773,plain,
    ! [X6193,X6194,X6195,X6196,X6197] :
      ( ~ linord20386208strict(X6193)
      | ~ hBOOL(hAPP(X6193,bool,hAPP(X6193,fun(X6193,bool),ord_less(X6193),X6196),X6197))
      | ~ hBOOL(hAPP(X6193,bool,hAPP(X6193,fun(X6193,bool),ord_less(X6193),X6194),X6195))
      | ~ hBOOL(hAPP(X6193,bool,hAPP(X6193,fun(X6193,bool),ord_less(X6193),zero_zero(X6193)),X6197))
      | ~ hBOOL(hAPP(X6193,bool,hAPP(X6193,fun(X6193,bool),ord_less_eq(X6193),zero_zero(X6193)),X6194))
      | hBOOL(hAPP(X6193,bool,hAPP(X6193,fun(X6193,bool),ord_less(X6193),hAPP(X6193,X6193,hAPP(X6193,fun(X6193,X6193),times_times(X6193),X6196),X6194)),hAPP(X6193,X6193,hAPP(X6193,fun(X6193,X6193),times_times(X6193),X6197),X6195))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_675_mult__strict__mono])])]) ).

fof(i_0_1774,plain,
    ! [X4848,X4849,X4850,X4851,X4852] :
      ( ( ~ hBOOL(hAPP(X4848,bool,hAPP(X4849,fun(X4848,bool),hAPP(fun(product_prod(X4849,X4848),bool),fun(X4849,fun(X4848,bool)),in_rel(X4849,X4848),X4850),X4851),X4852))
        | hBOOL(hAPP(fun(product_prod(X4849,X4848),bool),bool,hAPP(product_prod(X4849,X4848),fun(fun(product_prod(X4849,X4848),bool),bool),member(product_prod(X4849,X4848)),hAPP(X4848,product_prod(X4849,X4848),hAPP(X4849,fun(X4848,product_prod(X4849,X4848)),product_Pair(X4849,X4848),X4851),X4852)),X4850)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X4849,X4848),bool),bool,hAPP(product_prod(X4849,X4848),fun(fun(product_prod(X4849,X4848),bool),bool),member(product_prod(X4849,X4848)),hAPP(X4848,product_prod(X4849,X4848),hAPP(X4849,fun(X4848,product_prod(X4849,X4848)),product_Pair(X4849,X4848),X4851),X4852)),X4850))
        | hBOOL(hAPP(X4848,bool,hAPP(X4849,fun(X4848,bool),hAPP(fun(product_prod(X4849,X4848),bool),fun(X4849,fun(X4848,bool)),in_rel(X4849,X4848),X4850),X4851),X4852)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_in__rel__def])]) ).

fof(i_0_1775,plain,
    ! [X6263,X6264,X6265] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6263),X6264)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6265),X6264)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6264))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6263),X6265)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6264))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6263),X6264)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6265),X6264))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6263),X6265))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6263),X6264)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6265),X6264))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_695_mult__le__cancel2])])]) ).

fof(i_0_1776,plain,
    ! [X6301,X6302,X6303] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6303),X6301)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6303),X6302)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6301),X6302))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6303)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6301),X6302))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6303),X6301)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6303),X6302)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6303)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_704_nat__mult__le__cancel1])])]) ).

fof(i_0_1777,plain,
    ! [X6266,X6267,X6268] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6267)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6268)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6266))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6267),X6268)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6266))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6267)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6268))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6267),X6268))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6267)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6266),X6268))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_696_mult__le__cancel1])])]) ).

fof(i_0_1778,plain,
    ! [X6304,X6305,X6306] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6306),X6304)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6306),X6305)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6304),X6305))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6306)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6304),X6305))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6306),X6304)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6306),X6305)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6306)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_705_nat__mult__less__cancel1])])]) ).

fof(i_0_1779,plain,
    ! [X7367,X7368,X7369,X7370,X7371,X7372] :
      ( ~ hBOOL(hAPP(fun(X7367,bool),bool,hAPP(fun(X7367,X7368),fun(fun(X7367,bool),bool),inj_on(X7367,X7368),X7371),X7372))
      | ~ hBOOL(hAPP(fun(X7367,bool),bool,hAPP(fun(X7367,bool),fun(fun(X7367,bool),bool),ord_less_eq(fun(X7367,bool)),X7370),X7372))
      | ~ hBOOL(hAPP(fun(X7367,bool),bool,hAPP(fun(X7367,bool),fun(fun(X7367,bool),bool),ord_less_eq(fun(X7367,bool)),X7369),X7372))
      | hAPP(fun(X7367,bool),fun(X7368,bool),hAPP(fun(X7367,X7368),fun(fun(X7367,bool),fun(X7368,bool)),image(X7367,X7368),X7371),hAPP(fun(X7367,bool),fun(X7367,bool),hAPP(fun(X7367,bool),fun(fun(X7367,bool),fun(X7367,bool)),semilattice_inf_inf(fun(X7367,bool)),X7370),X7369)) = hAPP(fun(X7368,bool),fun(X7368,bool),hAPP(fun(X7368,bool),fun(fun(X7368,bool),fun(X7368,bool)),semilattice_inf_inf(fun(X7368,bool)),hAPP(fun(X7367,bool),fun(X7368,bool),hAPP(fun(X7367,X7368),fun(fun(X7367,bool),fun(X7368,bool)),image(X7367,X7368),X7371),X7370)),hAPP(fun(X7367,bool),fun(X7368,bool),hAPP(fun(X7367,X7368),fun(fun(X7367,bool),fun(X7368,bool)),image(X7367,X7368),X7371),X7369)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_957_inj__on__image__Int])]) ).

fof(i_0_1780,plain,
    ! [X6070,X6071,X6072,X6073] :
      ( ( hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6071),zero_zero(X6070)))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),zero_zero(X6070)),X6071))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) )
      & ( hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6073),X6072))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),zero_zero(X6070)),X6071))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) )
      & ( hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6071),zero_zero(X6070)))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6072),X6073))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) )
      & ( hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6073),X6072))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6072),X6073))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) )
      & ( ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),zero_zero(X6070)),X6071))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6072),X6073))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) )
      & ( ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6071),zero_zero(X6070)))
        | ~ hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),X6073),X6072))
        | hBOOL(hAPP(X6070,bool,hAPP(X6070,fun(X6070,bool),ord_less(X6070),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6072)),hAPP(X6070,X6070,hAPP(X6070,fun(X6070,X6070),times_times(X6070),X6071),X6073)))
        | ~ linord581940658strict(X6070) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_638_mult__less__cancel__left__disj])])])]) ).

fof(i_0_1781,plain,
    ! [X6066,X6067,X6068,X6069] :
      ( ( hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6068),zero_zero(X6066)))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),zero_zero(X6066)),X6068))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) )
      & ( hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6069),X6067))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),zero_zero(X6066)),X6068))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) )
      & ( hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6068),zero_zero(X6066)))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6067),X6069))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) )
      & ( hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6069),X6067))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6067),X6069))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) )
      & ( ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),zero_zero(X6066)),X6068))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6067),X6069))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) )
      & ( ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6068),zero_zero(X6066)))
        | ~ hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),X6069),X6067))
        | hBOOL(hAPP(X6066,bool,hAPP(X6066,fun(X6066,bool),ord_less(X6066),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6067),X6068)),hAPP(X6066,X6066,hAPP(X6066,fun(X6066,X6066),times_times(X6066),X6069),X6068)))
        | ~ linord581940658strict(X6066) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_637_mult__less__cancel__right__disj])])])]) ).

fof(i_0_1782,plain,
    ! [X4890,X4891] :
      ( ~ hBOOL(hAPP(fun(X4890,bool),bool,finite_finite_1(X4890),X4891))
      | hBOOL(hAPP(fun(fun(X4890,bool),bool),bool,finite_finite_1(fun(X4890,bool)),hAPP(fun(fun(X4890,bool),bool),fun(fun(X4890,bool),bool),collect(fun(X4890,bool)),hAPP(fun(X4890,bool),fun(fun(X4890,bool),bool),hAPP(fun(fun(X4890,bool),fun(fun(X4890,bool),bool)),fun(fun(X4890,bool),fun(fun(X4890,bool),bool)),combc(fun(X4890,bool),fun(X4890,bool),bool),ord_less_eq(fun(X4890,bool))),X4891)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_finite__Collect__subsets])]) ).

fof(i_0_1783,plain,
    ! [X7392,X7393,X7394] :
      ( ~ hBOOL(hAPP(fun(X7392,bool),bool,finite_finite_1(X7392),X7394))
      | ~ hBOOL(hAPP(fun(X7392,bool),bool,finite_finite_1(X7392),X7393))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7392,bool),nat,finite_card(X7392),hAPP(fun(X7392,bool),fun(X7392,bool),hAPP(fun(X7392,bool),fun(fun(X7392,bool),fun(X7392,bool)),semilattice_sup_sup(fun(X7392,bool)),X7394),X7393))),hAPP(fun(X7392,bool),nat,finite_card(X7392),hAPP(fun(X7392,bool),fun(X7392,bool),hAPP(fun(X7392,bool),fun(fun(X7392,bool),fun(X7392,bool)),semilattice_inf_inf(fun(X7392,bool)),X7394),X7393))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7392,bool),nat,finite_card(X7392),X7394)),hAPP(fun(X7392,bool),nat,finite_card(X7392),X7393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_963_card_Ounion__inter])]) ).

fof(i_0_1784,plain,
    ! [X7389,X7390,X7391] :
      ( ~ hBOOL(hAPP(fun(X7389,bool),bool,finite_finite_1(X7389),X7391))
      | ~ hBOOL(hAPP(fun(X7389,bool),bool,finite_finite_1(X7389),X7390))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7389,bool),nat,finite_card(X7389),X7391)),hAPP(fun(X7389,bool),nat,finite_card(X7389),X7390)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7389,bool),nat,finite_card(X7389),hAPP(fun(X7389,bool),fun(X7389,bool),hAPP(fun(X7389,bool),fun(fun(X7389,bool),fun(X7389,bool)),semilattice_sup_sup(fun(X7389,bool)),X7391),X7390))),hAPP(fun(X7389,bool),nat,finite_card(X7389),hAPP(fun(X7389,bool),fun(X7389,bool),hAPP(fun(X7389,bool),fun(fun(X7389,bool),fun(X7389,bool)),semilattice_inf_inf(fun(X7389,bool)),X7391),X7390))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_962_card__Un__Int])]) ).

fof(i_0_1785,plain,
    ! [X4178,X4179,X4180,X4181] :
      ( ~ hBOOL(hAPP(fun(X4179,bool),bool,hAPP(fun(X4179,X4180),fun(fun(X4179,bool),bool),inj_on(X4179,X4180),X4181),top_top(fun(X4179,bool))))
      | hBOOL(hAPP(fun(X4179,bool),bool,hAPP(fun(X4179,fun(X4178,X4180)),fun(fun(X4179,bool),bool),inj_on(X4179,fun(X4178,X4180)),hAPP(fun(X4179,X4180),fun(X4179,fun(X4178,X4180)),hAPP(fun(X4180,fun(X4178,X4180)),fun(fun(X4179,X4180),fun(X4179,fun(X4178,X4180))),combb(X4180,fun(X4178,X4180),X4179),combk(X4180,X4178)),X4181)),top_top(fun(X4179,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_inj__fun])]) ).

fof(i_0_1786,plain,
    ! [X7399,X7400,X7401,X7402] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X7401)),X7402))
        | hAPP(fun(nat,bool),X7399,hAPP(fun(nat,X7399),fun(fun(nat,bool),X7399),big_co1399186613setsum(nat,X7399),X7400),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7402),hAPP(nat,nat,suc,X7401))) = zero_zero(X7399)
        | ~ comm_monoid_add(X7399) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X7401)),X7402))
        | hAPP(fun(nat,bool),X7399,hAPP(fun(nat,X7399),fun(fun(nat,bool),X7399),big_co1399186613setsum(nat,X7399),X7400),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7402),hAPP(nat,nat,suc,X7401))) = hAPP(X7399,X7399,hAPP(X7399,fun(X7399,X7399),plus_plus(X7399),hAPP(fun(nat,bool),X7399,hAPP(fun(nat,X7399),fun(fun(nat,bool),X7399),big_co1399186613setsum(nat,X7399),X7400),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7402),X7401))),hAPP(nat,X7399,X7400,hAPP(nat,nat,suc,X7401)))
        | ~ comm_monoid_add(X7399) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1223])])])]) ).

cnf(i_0_1787,plain,
    ( hAPP(fun(X1,X2),fun(X1,X4),hAPP(fun(X2,X4),fun(fun(X1,X2),fun(X1,X4)),comp(X2,X4,X1),hAPP(fun(X2,X1),fun(X2,X4),hAPP(fun(X1,X4),fun(fun(X2,X1),fun(X2,X4)),comp(X1,X4,X2),X5),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))),X3) = ti(fun(X1,X4),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_1224]) ).

fof(i_0_1788,plain,
    ! [X6999,X7000,X7001,X7002,X7003,X7004] :
      ( ~ hBOOL(hAPP(X6999,bool,hAPP(X7000,fun(X6999,bool),X7002,X7003),X7004))
      | hBOOL(hAPP(X6999,bool,hAPP(X7000,fun(X6999,bool),hAPP(fun(X7000,fun(X6999,bool)),fun(X7000,fun(X6999,bool)),hAPP(fun(X7000,fun(X6999,bool)),fun(fun(X7000,fun(X6999,bool)),fun(X7000,fun(X6999,bool))),semilattice_sup_sup(fun(X7000,fun(X6999,bool))),X7002),X7001),X7003),X7004)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_858_sup2I1])]) ).

fof(i_0_1789,plain,
    ! [X6993,X6994,X6995,X6996,X6997,X6998] :
      ( ( ~ hBOOL(hAPP(X6993,bool,hAPP(X6994,fun(X6993,bool),X6996,X6997),X6998))
        | hBOOL(hAPP(X6993,bool,hAPP(X6994,fun(X6993,bool),hAPP(fun(X6994,fun(X6993,bool)),fun(X6994,fun(X6993,bool)),hAPP(fun(X6994,fun(X6993,bool)),fun(fun(X6994,fun(X6993,bool)),fun(X6994,fun(X6993,bool))),semilattice_sup_sup(fun(X6994,fun(X6993,bool))),X6995),X6996),X6997),X6998)) )
      & ( ~ hBOOL(hAPP(X6993,bool,hAPP(X6994,fun(X6993,bool),X6995,X6997),X6998))
        | hBOOL(hAPP(X6993,bool,hAPP(X6994,fun(X6993,bool),hAPP(fun(X6994,fun(X6993,bool)),fun(X6994,fun(X6993,bool)),hAPP(fun(X6994,fun(X6993,bool)),fun(fun(X6994,fun(X6993,bool)),fun(X6994,fun(X6993,bool))),semilattice_sup_sup(fun(X6994,fun(X6993,bool))),X6995),X6996),X6997),X6998)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1225])])]) ).

fof(i_0_1790,plain,
    ! [X7005,X7006,X7007,X7008,X7009,X7010] :
      ( ~ hBOOL(hAPP(X7005,bool,hAPP(X7006,fun(X7005,bool),X7008,X7009),X7010))
      | hBOOL(hAPP(X7005,bool,hAPP(X7006,fun(X7005,bool),hAPP(fun(X7006,fun(X7005,bool)),fun(X7006,fun(X7005,bool)),hAPP(fun(X7006,fun(X7005,bool)),fun(fun(X7006,fun(X7005,bool)),fun(X7006,fun(X7005,bool))),semilattice_sup_sup(fun(X7006,fun(X7005,bool))),X7007),X7008),X7009),X7010)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_859_sup2I2])]) ).

fof(i_0_1791,plain,
    ! [X4041,X4042] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4042),arrow_1568854078le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4042),X4041)),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_mktop__Lin])]) ).

fof(i_0_1792,plain,
    ! [X4043,X4044] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4044),arrow_1568854078le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4044),X4043)),arrow_1568854078le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_mkbot__Lin])]) ).

fof(i_0_1793,plain,
    ! [X5749,X5750,X5751,X5752] :
      ( ( ~ hBOOL(hAPP(fun(X5749,bool),bool,hAPP(fun(X5749,X5750),fun(fun(X5749,bool),bool),inj_on(X5749,X5750),hAPP(fun(X5749,bool),fun(X5749,X5750),hAPP(fun(X5749,X5750),fun(fun(X5749,bool),fun(X5749,X5750)),restrict(X5749,X5750),X5751),X5752)),X5752))
        | hBOOL(hAPP(fun(X5749,bool),bool,hAPP(fun(X5749,X5750),fun(fun(X5749,bool),bool),inj_on(X5749,X5750),X5751),X5752)) )
      & ( ~ hBOOL(hAPP(fun(X5749,bool),bool,hAPP(fun(X5749,X5750),fun(fun(X5749,bool),bool),inj_on(X5749,X5750),X5751),X5752))
        | hBOOL(hAPP(fun(X5749,bool),bool,hAPP(fun(X5749,X5750),fun(fun(X5749,bool),bool),inj_on(X5749,X5750),hAPP(fun(X5749,bool),fun(X5749,X5750),hAPP(fun(X5749,X5750),fun(fun(X5749,bool),fun(X5749,X5750)),restrict(X5749,X5750),X5751),X5752)),X5752)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_551_inj__on__restrict__eq])]) ).

fof(i_0_1794,plain,
    ! [X6386,X6387,X6388,X6389,X6390] :
      ( ~ hBOOL(hAPP(fun(X6387,bool),bool,hAPP(fun(X6387,X6388),fun(fun(X6387,bool),bool),inj_on(X6387,X6388),X6390),top_top(fun(X6387,bool))))
      | ~ hBOOL(hAPP(fun(X6386,bool),bool,hAPP(fun(X6386,X6387),fun(fun(X6386,bool),bool),inj_on(X6386,X6387),X6389),top_top(fun(X6386,bool))))
      | hBOOL(hAPP(fun(X6386,bool),bool,hAPP(fun(X6386,X6388),fun(fun(X6386,bool),bool),inj_on(X6386,X6388),hAPP(fun(X6386,X6387),fun(X6386,X6388),hAPP(fun(X6387,X6388),fun(fun(X6386,X6387),fun(X6386,X6388)),comp(X6387,X6388,X6386),X6390),X6389)),top_top(fun(X6386,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_721_inj__comp])]) ).

fof(i_0_1795,plain,
    ! [X4526,X4527,X4528,X4529] :
      ( ( ~ hBOOL(hAPP(X4526,bool,hAPP(X4526,fun(X4526,bool),ord_less_eq(X4526),hAPP(X4526,X4526,hAPP(X4526,fun(X4526,X4526),plus_plus(X4526),X4527),X4528)),hAPP(X4526,X4526,hAPP(X4526,fun(X4526,X4526),plus_plus(X4526),X4529),X4528)))
        | hBOOL(hAPP(X4526,bool,hAPP(X4526,fun(X4526,bool),ord_less_eq(X4526),X4527),X4529))
        | ~ ordere236663937imp_le(X4526) )
      & ( ~ hBOOL(hAPP(X4526,bool,hAPP(X4526,fun(X4526,bool),ord_less_eq(X4526),X4527),X4529))
        | hBOOL(hAPP(X4526,bool,hAPP(X4526,fun(X4526,bool),ord_less_eq(X4526),hAPP(X4526,X4526,hAPP(X4526,fun(X4526,X4526),plus_plus(X4526),X4527),X4528)),hAPP(X4526,X4526,hAPP(X4526,fun(X4526,X4526),plus_plus(X4526),X4529),X4528)))
        | ~ ordere236663937imp_le(X4526) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_add__le__cancel__right])])])]) ).

fof(i_0_1796,plain,
    ! [X4505,X4506,X4507,X4508] :
      ( ~ ordere236663937imp_le(X4505)
      | ~ hBOOL(hAPP(X4505,bool,hAPP(X4505,fun(X4505,bool),ord_less_eq(X4505),hAPP(X4505,X4505,hAPP(X4505,fun(X4505,X4505),plus_plus(X4505),X4506),X4507)),hAPP(X4505,X4505,hAPP(X4505,fun(X4505,X4505),plus_plus(X4505),X4508),X4507)))
      | hBOOL(hAPP(X4505,bool,hAPP(X4505,fun(X4505,bool),ord_less_eq(X4505),X4506),X4508)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_add__le__imp__le__right])])]) ).

fof(i_0_1797,plain,
    ! [X4522,X4523,X4524,X4525] :
      ( ( ~ hBOOL(hAPP(X4522,bool,hAPP(X4522,fun(X4522,bool),ord_less_eq(X4522),hAPP(X4522,X4522,hAPP(X4522,fun(X4522,X4522),plus_plus(X4522),X4523),X4524)),hAPP(X4522,X4522,hAPP(X4522,fun(X4522,X4522),plus_plus(X4522),X4523),X4525)))
        | hBOOL(hAPP(X4522,bool,hAPP(X4522,fun(X4522,bool),ord_less_eq(X4522),X4524),X4525))
        | ~ ordere236663937imp_le(X4522) )
      & ( ~ hBOOL(hAPP(X4522,bool,hAPP(X4522,fun(X4522,bool),ord_less_eq(X4522),X4524),X4525))
        | hBOOL(hAPP(X4522,bool,hAPP(X4522,fun(X4522,bool),ord_less_eq(X4522),hAPP(X4522,X4522,hAPP(X4522,fun(X4522,X4522),plus_plus(X4522),X4523),X4524)),hAPP(X4522,X4522,hAPP(X4522,fun(X4522,X4522),plus_plus(X4522),X4523),X4525)))
        | ~ ordere236663937imp_le(X4522) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_add__le__cancel__left])])])]) ).

fof(i_0_1798,plain,
    ! [X4501,X4502,X4503,X4504] :
      ( ~ ordere236663937imp_le(X4501)
      | ~ hBOOL(hAPP(X4501,bool,hAPP(X4501,fun(X4501,bool),ord_less_eq(X4501),hAPP(X4501,X4501,hAPP(X4501,fun(X4501,X4501),plus_plus(X4501),X4502),X4503)),hAPP(X4501,X4501,hAPP(X4501,fun(X4501,X4501),plus_plus(X4501),X4502),X4504)))
      | hBOOL(hAPP(X4501,bool,hAPP(X4501,fun(X4501,bool),ord_less_eq(X4501),X4503),X4504)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_172_add__le__imp__le__left])])]) ).

fof(i_0_1799,plain,
    ! [X4555,X4556,X4557,X4558] :
      ( ( ~ hBOOL(hAPP(X4555,bool,hAPP(X4555,fun(X4555,bool),ord_less(X4555),hAPP(X4555,X4555,hAPP(X4555,fun(X4555,X4555),plus_plus(X4555),X4556),X4557)),hAPP(X4555,X4555,hAPP(X4555,fun(X4555,X4555),plus_plus(X4555),X4558),X4557)))
        | hBOOL(hAPP(X4555,bool,hAPP(X4555,fun(X4555,bool),ord_less(X4555),X4556),X4558))
        | ~ ordere236663937imp_le(X4555) )
      & ( ~ hBOOL(hAPP(X4555,bool,hAPP(X4555,fun(X4555,bool),ord_less(X4555),X4556),X4558))
        | hBOOL(hAPP(X4555,bool,hAPP(X4555,fun(X4555,bool),ord_less(X4555),hAPP(X4555,X4555,hAPP(X4555,fun(X4555,X4555),plus_plus(X4555),X4556),X4557)),hAPP(X4555,X4555,hAPP(X4555,fun(X4555,X4555),plus_plus(X4555),X4558),X4557)))
        | ~ ordere236663937imp_le(X4555) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_185_add__less__cancel__right])])])]) ).

fof(i_0_1800,plain,
    ! [X4534,X4535,X4536,X4537] :
      ( ~ ordere236663937imp_le(X4534)
      | ~ hBOOL(hAPP(X4534,bool,hAPP(X4534,fun(X4534,bool),ord_less(X4534),hAPP(X4534,X4534,hAPP(X4534,fun(X4534,X4534),plus_plus(X4534),X4535),X4536)),hAPP(X4534,X4534,hAPP(X4534,fun(X4534,X4534),plus_plus(X4534),X4537),X4536)))
      | hBOOL(hAPP(X4534,bool,hAPP(X4534,fun(X4534,bool),ord_less(X4534),X4535),X4537)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_add__less__imp__less__right])])]) ).

fof(i_0_1801,plain,
    ! [X4551,X4552,X4553,X4554] :
      ( ( ~ hBOOL(hAPP(X4551,bool,hAPP(X4551,fun(X4551,bool),ord_less(X4551),hAPP(X4551,X4551,hAPP(X4551,fun(X4551,X4551),plus_plus(X4551),X4552),X4553)),hAPP(X4551,X4551,hAPP(X4551,fun(X4551,X4551),plus_plus(X4551),X4552),X4554)))
        | hBOOL(hAPP(X4551,bool,hAPP(X4551,fun(X4551,bool),ord_less(X4551),X4553),X4554))
        | ~ ordere236663937imp_le(X4551) )
      & ( ~ hBOOL(hAPP(X4551,bool,hAPP(X4551,fun(X4551,bool),ord_less(X4551),X4553),X4554))
        | hBOOL(hAPP(X4551,bool,hAPP(X4551,fun(X4551,bool),ord_less(X4551),hAPP(X4551,X4551,hAPP(X4551,fun(X4551,X4551),plus_plus(X4551),X4552),X4553)),hAPP(X4551,X4551,hAPP(X4551,fun(X4551,X4551),plus_plus(X4551),X4552),X4554)))
        | ~ ordere236663937imp_le(X4551) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_add__less__cancel__left])])])]) ).

fof(i_0_1802,plain,
    ! [X4530,X4531,X4532,X4533] :
      ( ~ ordere236663937imp_le(X4530)
      | ~ hBOOL(hAPP(X4530,bool,hAPP(X4530,fun(X4530,bool),ord_less(X4530),hAPP(X4530,X4530,hAPP(X4530,fun(X4530,X4530),plus_plus(X4530),X4531),X4532)),hAPP(X4530,X4530,hAPP(X4530,fun(X4530,X4530),plus_plus(X4530),X4531),X4533)))
      | hBOOL(hAPP(X4530,bool,hAPP(X4530,fun(X4530,bool),ord_less(X4530),X4532),X4533)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_add__less__imp__less__left])])]) ).

fof(i_0_1803,plain,
    ! [X6807,X6808,X6809] : hAPP(fun(X6807,bool),fun(X6807,bool),collect(X6807),hAPP(fun(X6807,bool),fun(X6807,bool),hAPP(fun(X6807,fun(bool,bool)),fun(fun(X6807,bool),fun(X6807,bool)),combs(X6807,bool,bool),hAPP(fun(X6807,bool),fun(X6807,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X6807,bool),fun(X6807,fun(bool,bool))),combb(bool,fun(bool,bool),X6807),fdisj),X6808)),X6809)) = hAPP(fun(X6807,bool),fun(X6807,bool),hAPP(fun(X6807,bool),fun(fun(X6807,bool),fun(X6807,bool)),semilattice_sup_sup(fun(X6807,bool)),hAPP(fun(X6807,bool),fun(X6807,bool),collect(X6807),X6808)),hAPP(fun(X6807,bool),fun(X6807,bool),collect(X6807),X6809)),
    inference(variable_rename,[status(thm)],[fact_805_Collect__disj__eq]) ).

fof(i_0_1804,plain,
    ! [X7144,X7145,X7146] : hAPP(fun(X7144,bool),fun(X7144,bool),collect(X7144),hAPP(fun(X7144,bool),fun(X7144,bool),hAPP(fun(X7144,fun(bool,bool)),fun(fun(X7144,bool),fun(X7144,bool)),combs(X7144,bool,bool),hAPP(fun(X7144,bool),fun(X7144,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X7144,bool),fun(X7144,fun(bool,bool))),combb(bool,fun(bool,bool),X7144),fconj),X7145)),X7146)) = hAPP(fun(X7144,bool),fun(X7144,bool),hAPP(fun(X7144,bool),fun(fun(X7144,bool),fun(X7144,bool)),semilattice_inf_inf(fun(X7144,bool)),hAPP(fun(X7144,bool),fun(X7144,bool),collect(X7144),X7145)),hAPP(fun(X7144,bool),fun(X7144,bool),collect(X7144),X7146)),
    inference(variable_rename,[status(thm)],[fact_895_Collect__conj__eq]) ).

fof(i_0_1805,plain,
    ! [X5339,X5340,X5341,X5342,X5343] :
      ( ~ hBOOL(hAPP(fun(X5340,bool),bool,hAPP(fun(X5340,bool),fun(fun(X5340,bool),bool),ord_less_eq(fun(X5340,bool)),X5342),X5343))
      | hBOOL(hAPP(fun(X5339,bool),bool,hAPP(fun(X5339,bool),fun(fun(X5339,bool),bool),ord_less_eq(fun(X5339,bool)),hAPP(fun(X5340,bool),fun(X5339,bool),hAPP(fun(X5340,X5339),fun(fun(X5340,bool),fun(X5339,bool)),image(X5340,X5339),X5341),X5342)),hAPP(fun(X5340,bool),fun(X5339,bool),hAPP(fun(X5340,X5339),fun(fun(X5340,bool),fun(X5339,bool)),image(X5340,X5339),X5341),X5343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_462_image__mono])]) ).

cnf(i_0_1806,plain,
    ( hAPP(fun(X2,X1),fun(X2,X2),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(X2,X2)),hAPP(fun(X2,bool),fun(fun(X1,X2),fun(fun(X2,X1),fun(X2,X2))),compose(X2,X1,X2),X5),X3),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(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)),X5)) = hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X5)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1226]) ).

fof(i_0_1807,plain,
    ! [X5770,X5771,X5772,X5773] :
      ( ~ hBOOL(hAPP(fun(X5770,bool),bool,hAPP(fun(X5770,X5771),fun(fun(X5770,bool),bool),inj_on(X5770,X5771),X5772),X5773))
      | hBOOL(hAPP(fun(X5771,bool),bool,hAPP(fun(X5771,X5770),fun(fun(X5771,bool),bool),inj_on(X5771,X5770),hAPP(fun(X5770,X5771),fun(X5771,X5770),hAPP(fun(X5770,bool),fun(fun(X5770,X5771),fun(X5771,X5770)),the_inv_into(X5770,X5771),X5773),X5772)),hAPP(fun(X5770,bool),fun(X5771,bool),hAPP(fun(X5770,X5771),fun(fun(X5770,bool),fun(X5771,bool)),image(X5770,X5771),X5772),X5773))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_556_inj__on__the__inv__into])]) ).

fof(i_0_1808,plain,
    ! [X6154,X6155,X6156] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6154))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6155)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6156))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6155),X6156))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6155)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6156))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6154))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6155),X6156))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6155)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6154),X6156))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_663_mult__less__cancel1])])]) ).

fof(i_0_1809,plain,
    ! [X6151,X6152,X6153] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6152))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6151),X6152)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6153),X6152))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6151),X6153))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6151),X6152)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6153),X6152))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6152))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6151),X6153))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6151),X6152)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6153),X6152))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_662_mult__less__cancel2])])]) ).

fof(i_0_1810,plain,
    ! [X4778,X4779,X4780] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4778),X4779)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4778),X4780)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4779),X4780)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4779),X4780))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4778),X4779)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4778),X4780))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_nat__add__left__cancel__le])]) ).

fof(i_0_1811,plain,
    ! [X4735,X4736,X4737] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4735),X4736)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4735),X4737)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4736),X4737)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4736),X4737))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4735),X4736)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4735),X4737))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_235_nat__add__left__cancel__less])]) ).

cnf(i_0_1812,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | ti(X1,X3) = ti(X1,X5)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1227]) ).

cnf(i_0_1813,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1228]) ).

cnf(i_0_1814,plain,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X4),X3),X5)) = ti(X2,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,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1229]) ).

fof(i_0_1815,plain,
    ! [X4559,X4560,X4561,X4562] :
      ( ~ ord(X4560)
      | ~ hBOOL(hAPP(X4560,bool,hAPP(X4560,fun(X4560,bool),ord_less_eq(X4560),hAPP(X4559,X4560,X4561,esk43_4(X4559,X4560,X4561,X4562))),hAPP(X4559,X4560,X4562,esk43_4(X4559,X4560,X4561,X4562))))
      | hBOOL(hAPP(fun(X4559,X4560),bool,hAPP(fun(X4559,X4560),fun(fun(X4559,X4560),bool),ord_less_eq(fun(X4559,X4560)),X4561),X4562)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_le__funI])])])]) ).

fof(i_0_1816,plain,
    ! [X4248,X4249,X4250,X4251,X4252,X4253,X4254] :
      ( ( ~ hBOOL(hAPP(fun(X4248,X4249),bool,hAPP(fun(X4248,X4249),fun(fun(X4248,X4249),bool),ord_less_eq(fun(X4248,X4249)),X4250),X4251))
        | hBOOL(hAPP(X4249,bool,hAPP(X4249,fun(X4249,bool),ord_less_eq(X4249),hAPP(X4248,X4249,X4250,X4252)),hAPP(X4248,X4249,X4251,X4252)))
        | ~ ord(X4249) )
      & ( ~ hBOOL(hAPP(X4249,bool,hAPP(X4249,fun(X4249,bool),ord_less_eq(X4249),hAPP(X4248,X4249,X4253,esk30_4(X4248,X4249,X4253,X4254))),hAPP(X4248,X4249,X4254,esk30_4(X4248,X4249,X4253,X4254))))
        | hBOOL(hAPP(fun(X4248,X4249),bool,hAPP(fun(X4248,X4249),fun(fun(X4248,X4249),bool),ord_less_eq(fun(X4248,X4249)),X4253),X4254))
        | ~ ord(X4249) ) ),
    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_110_le__fun__def])])])])])]) ).

fof(i_0_1817,plain,
    ! [X6759,X6760,X6761,X6762,X6763,X6766,X6767,X6768,X6769,X6770,X6771] :
      ( ( hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),esk167_4(X6759,X6760,X6761,X6762)),X6762))
        | hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),esk166_4(X6759,X6760,X6761,X6762)),X6761))
        | ~ hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),X6763),hAPP(fun(X6759,bool),fun(X6759,bool),hAPP(fun(X6759,bool),fun(fun(X6759,bool),fun(X6759,bool)),semilattice_sup_sup(fun(X6759,bool)),X6761),X6762)))
        | ~ hBOOL(hAPP(X6759,bool,X6760,X6763)) )
      & ( hBOOL(hAPP(X6759,bool,X6760,esk167_4(X6759,X6760,X6761,X6762)))
        | hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),esk166_4(X6759,X6760,X6761,X6762)),X6761))
        | ~ hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),X6763),hAPP(fun(X6759,bool),fun(X6759,bool),hAPP(fun(X6759,bool),fun(fun(X6759,bool),fun(X6759,bool)),semilattice_sup_sup(fun(X6759,bool)),X6761),X6762)))
        | ~ hBOOL(hAPP(X6759,bool,X6760,X6763)) )
      & ( hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),esk167_4(X6759,X6760,X6761,X6762)),X6762))
        | hBOOL(hAPP(X6759,bool,X6760,esk166_4(X6759,X6760,X6761,X6762)))
        | ~ hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),X6763),hAPP(fun(X6759,bool),fun(X6759,bool),hAPP(fun(X6759,bool),fun(fun(X6759,bool),fun(X6759,bool)),semilattice_sup_sup(fun(X6759,bool)),X6761),X6762)))
        | ~ hBOOL(hAPP(X6759,bool,X6760,X6763)) )
      & ( hBOOL(hAPP(X6759,bool,X6760,esk167_4(X6759,X6760,X6761,X6762)))
        | hBOOL(hAPP(X6759,bool,X6760,esk166_4(X6759,X6760,X6761,X6762)))
        | ~ hBOOL(hAPP(fun(X6759,bool),bool,hAPP(X6759,fun(fun(X6759,bool),bool),member(X6759),X6763),hAPP(fun(X6759,bool),fun(X6759,bool),hAPP(fun(X6759,bool),fun(fun(X6759,bool),fun(X6759,bool)),semilattice_sup_sup(fun(X6759,bool)),X6761),X6762)))
        | ~ hBOOL(hAPP(X6759,bool,X6760,X6763)) )
      & ( hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),esk168_4(X6766,X6767,X6768,X6769)),hAPP(fun(X6766,bool),fun(X6766,bool),hAPP(fun(X6766,bool),fun(fun(X6766,bool),fun(X6766,bool)),semilattice_sup_sup(fun(X6766,bool)),X6768),X6769)))
        | ~ hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),X6770),X6768))
        | ~ hBOOL(hAPP(X6766,bool,X6767,X6770)) )
      & ( hBOOL(hAPP(X6766,bool,X6767,esk168_4(X6766,X6767,X6768,X6769)))
        | ~ hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),X6770),X6768))
        | ~ hBOOL(hAPP(X6766,bool,X6767,X6770)) )
      & ( hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),esk168_4(X6766,X6767,X6768,X6769)),hAPP(fun(X6766,bool),fun(X6766,bool),hAPP(fun(X6766,bool),fun(fun(X6766,bool),fun(X6766,bool)),semilattice_sup_sup(fun(X6766,bool)),X6768),X6769)))
        | ~ hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),X6771),X6769))
        | ~ hBOOL(hAPP(X6766,bool,X6767,X6771)) )
      & ( hBOOL(hAPP(X6766,bool,X6767,esk168_4(X6766,X6767,X6768,X6769)))
        | ~ hBOOL(hAPP(fun(X6766,bool),bool,hAPP(X6766,fun(fun(X6766,bool),bool),member(X6766),X6771),X6769))
        | ~ hBOOL(hAPP(X6766,bool,X6767,X6771)) ) ),
    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_798_bex__Un])])])])])]) ).

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(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),X4),X3)),X6)) = ti(fun(X2,bool),X6)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4) != ti(fun(X2,bool),X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1230]) ).

fof(i_0_1819,plain,
    ! [X6773,X6774,X6775,X6776,X6778,X6779,X6780,X6781,X6782,X6783,X6786] :
      ( ( ~ hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),X6778),X6775))
        | hBOOL(hAPP(X6773,bool,X6774,X6778))
        | hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),esk169_4(X6773,X6774,X6775,X6776)),hAPP(fun(X6773,bool),fun(X6773,bool),hAPP(fun(X6773,bool),fun(fun(X6773,bool),fun(X6773,bool)),semilattice_sup_sup(fun(X6773,bool)),X6775),X6776))) )
      & ( ~ hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),X6779),X6776))
        | hBOOL(hAPP(X6773,bool,X6774,X6779))
        | hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),esk169_4(X6773,X6774,X6775,X6776)),hAPP(fun(X6773,bool),fun(X6773,bool),hAPP(fun(X6773,bool),fun(fun(X6773,bool),fun(X6773,bool)),semilattice_sup_sup(fun(X6773,bool)),X6775),X6776))) )
      & ( ~ hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),X6778),X6775))
        | hBOOL(hAPP(X6773,bool,X6774,X6778))
        | ~ hBOOL(hAPP(X6773,bool,X6774,esk169_4(X6773,X6774,X6775,X6776))) )
      & ( ~ hBOOL(hAPP(fun(X6773,bool),bool,hAPP(X6773,fun(fun(X6773,bool),bool),member(X6773),X6779),X6776))
        | hBOOL(hAPP(X6773,bool,X6774,X6779))
        | ~ hBOOL(hAPP(X6773,bool,X6774,esk169_4(X6773,X6774,X6775,X6776))) )
      & ( hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),esk171_4(X6780,X6781,X6782,X6783)),X6783))
        | hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),esk170_4(X6780,X6781,X6782,X6783)),X6782))
        | ~ hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),X6786),hAPP(fun(X6780,bool),fun(X6780,bool),hAPP(fun(X6780,bool),fun(fun(X6780,bool),fun(X6780,bool)),semilattice_sup_sup(fun(X6780,bool)),X6782),X6783)))
        | hBOOL(hAPP(X6780,bool,X6781,X6786)) )
      & ( ~ hBOOL(hAPP(X6780,bool,X6781,esk171_4(X6780,X6781,X6782,X6783)))
        | hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),esk170_4(X6780,X6781,X6782,X6783)),X6782))
        | ~ hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),X6786),hAPP(fun(X6780,bool),fun(X6780,bool),hAPP(fun(X6780,bool),fun(fun(X6780,bool),fun(X6780,bool)),semilattice_sup_sup(fun(X6780,bool)),X6782),X6783)))
        | hBOOL(hAPP(X6780,bool,X6781,X6786)) )
      & ( hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),esk171_4(X6780,X6781,X6782,X6783)),X6783))
        | ~ hBOOL(hAPP(X6780,bool,X6781,esk170_4(X6780,X6781,X6782,X6783)))
        | ~ hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),X6786),hAPP(fun(X6780,bool),fun(X6780,bool),hAPP(fun(X6780,bool),fun(fun(X6780,bool),fun(X6780,bool)),semilattice_sup_sup(fun(X6780,bool)),X6782),X6783)))
        | hBOOL(hAPP(X6780,bool,X6781,X6786)) )
      & ( ~ hBOOL(hAPP(X6780,bool,X6781,esk171_4(X6780,X6781,X6782,X6783)))
        | ~ hBOOL(hAPP(X6780,bool,X6781,esk170_4(X6780,X6781,X6782,X6783)))
        | ~ hBOOL(hAPP(fun(X6780,bool),bool,hAPP(X6780,fun(fun(X6780,bool),bool),member(X6780),X6786),hAPP(fun(X6780,bool),fun(X6780,bool),hAPP(fun(X6780,bool),fun(fun(X6780,bool),fun(X6780,bool)),semilattice_sup_sup(fun(X6780,bool)),X6782),X6783)))
        | hBOOL(hAPP(X6780,bool,X6781,X6786)) ) ),
    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_799_ball__Un])])])])])]) ).

fof(i_0_1820,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(i_0_1821,plain,
    ! [X5449,X5450,X5451,X5452,X5453] :
      ( ( ~ hBOOL(hAPP(fun(X5450,bool),bool,hAPP(X5450,fun(fun(X5450,bool),bool),member(X5450),hAPP(X5449,X5450,X5453,X5451)),hAPP(fun(X5449,bool),fun(X5450,bool),hAPP(fun(X5449,X5450),fun(fun(X5449,bool),fun(X5450,bool)),image(X5449,X5450),X5453),X5452)))
        | hBOOL(hAPP(fun(X5449,bool),bool,hAPP(X5449,fun(fun(X5449,bool),bool),member(X5449),X5451),X5452))
        | ~ hBOOL(hAPP(fun(X5449,bool),bool,hAPP(fun(X5449,X5450),fun(fun(X5449,bool),bool),inj_on(X5449,X5450),X5453),top_top(fun(X5449,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X5449,bool),bool,hAPP(X5449,fun(fun(X5449,bool),bool),member(X5449),X5451),X5452))
        | hBOOL(hAPP(fun(X5450,bool),bool,hAPP(X5450,fun(fun(X5450,bool),bool),member(X5450),hAPP(X5449,X5450,X5453,X5451)),hAPP(fun(X5449,bool),fun(X5450,bool),hAPP(fun(X5449,X5450),fun(fun(X5449,bool),fun(X5450,bool)),image(X5449,X5450),X5453),X5452)))
        | ~ hBOOL(hAPP(fun(X5449,bool),bool,hAPP(fun(X5449,X5450),fun(fun(X5449,bool),bool),inj_on(X5449,X5450),X5453),top_top(fun(X5449,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_481_inj__image__mem__iff])])]) ).

fof(i_0_1822,plain,
    ! [X6721,X6722,X6723,X6724] :
      ( ~ hBOOL(hAPP(fun(X6721,bool),bool,hAPP(fun(X6721,bool),fun(fun(X6721,bool),bool),ord_less_eq(fun(X6721,bool)),X6723),X6724))
      | ~ hBOOL(hAPP(fun(X6721,bool),bool,hAPP(fun(X6721,bool),fun(fun(X6721,bool),bool),ord_less_eq(fun(X6721,bool)),X6722),X6724))
      | hBOOL(hAPP(fun(X6721,bool),bool,hAPP(fun(X6721,bool),fun(fun(X6721,bool),bool),ord_less_eq(fun(X6721,bool)),hAPP(fun(X6721,bool),fun(X6721,bool),hAPP(fun(X6721,bool),fun(fun(X6721,bool),fun(X6721,bool)),semilattice_sup_sup(fun(X6721,bool)),X6723),X6722)),X6724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_787_Un__least])]) ).

fof(i_0_1823,plain,
    ! [X6261,X6262] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6261))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6261),X6262))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6262))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6261),X6262))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6261))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6262))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6261),X6262))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_694_one__le__mult__iff])])]) ).

fof(i_0_1824,plain,
    ! [X6259,X6260] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6260))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6259))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6259),X6260))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_693_one__less__mult])]) ).

fof(i_0_1825,plain,
    ! [X7395,X7396,X7397,X7398] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X7397),X7398))
        | hAPP(fun(nat,bool),X7395,hAPP(fun(nat,X7395),fun(fun(nat,bool),X7395),big_co1399186613setsum(nat,X7395),X7396),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7398),hAPP(nat,nat,suc,X7397))) = zero_zero(X7395)
        | ~ comm_monoid_add(X7395) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X7397),X7398))
        | hAPP(fun(nat,bool),X7395,hAPP(fun(nat,X7395),fun(fun(nat,bool),X7395),big_co1399186613setsum(nat,X7395),X7396),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7398),hAPP(nat,nat,suc,X7397))) = hAPP(X7395,X7395,hAPP(X7395,fun(X7395,X7395),plus_plus(X7395),hAPP(fun(nat,bool),X7395,hAPP(fun(nat,X7395),fun(fun(nat,bool),X7395),big_co1399186613setsum(nat,X7395),X7396),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7398),X7397))),hAPP(nat,X7395,X7396,X7397))
        | ~ comm_monoid_add(X7395) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1231])])])]) ).

fof(i_0_1826,plain,
    ! [X4048] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4048),arrow_1568854078le_Lin))
      | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X4048)),arrow_301600364e_Prof)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_const__Lin__Prof])]) ).

fof(i_0_1827,plain,
    ! [X6280,X6281,X6282] :
      ( ( hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less(X6280),zero_zero(X6280)),esk135_3(X6280,X6281,X6282)))
        | hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less_eq(X6280),X6281),X6282))
        | ~ linord1117847801e_zero(X6280) )
      & ( hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less(X6280),esk135_3(X6280,X6281,X6282)),one_one(X6280)))
        | hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less_eq(X6280),X6281),X6282))
        | ~ linord1117847801e_zero(X6280) )
      & ( ~ hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less_eq(X6280),hAPP(X6280,X6280,hAPP(X6280,fun(X6280,X6280),times_times(X6280),esk135_3(X6280,X6281,X6282)),X6281)),X6282))
        | hBOOL(hAPP(X6280,bool,hAPP(X6280,fun(X6280,bool),ord_less_eq(X6280),X6281),X6282))
        | ~ linord1117847801e_zero(X6280) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_699_field__le__mult__one__interval])])])])]) ).

fof(i_0_1828,plain,
    ! [X7061,X7062,X7063,X7064] :
      ( ( hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_sup_sup(fun(X7061,bool)),hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_inf_inf(fun(X7061,bool)),X7062),X7063)),X7064) != hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_inf_inf(fun(X7061,bool)),X7062),hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_sup_sup(fun(X7061,bool)),X7063),X7064))
        | hBOOL(hAPP(fun(X7061,bool),bool,hAPP(fun(X7061,bool),fun(fun(X7061,bool),bool),ord_less_eq(fun(X7061,bool)),X7064),X7062)) )
      & ( ~ hBOOL(hAPP(fun(X7061,bool),bool,hAPP(fun(X7061,bool),fun(fun(X7061,bool),bool),ord_less_eq(fun(X7061,bool)),X7064),X7062))
        | hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_sup_sup(fun(X7061,bool)),hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_inf_inf(fun(X7061,bool)),X7062),X7063)),X7064) = hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_inf_inf(fun(X7061,bool)),X7062),hAPP(fun(X7061,bool),fun(X7061,bool),hAPP(fun(X7061,bool),fun(fun(X7061,bool),fun(X7061,bool)),semilattice_sup_sup(fun(X7061,bool)),X7063),X7064)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_875_Un__Int__assoc__eq])]) ).

fof(i_0_1829,plain,
    ! [X5013,X5014,X5015,X5016,X5017] :
      ( ( ~ hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5015),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5016),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(X5014,fun(fun(X5014,bool),bool),member(X5014),esk79_5(X5013,X5014,X5015,X5016,X5017)),X5017)) )
      & ( ~ hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5016),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5015),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(X5014,fun(fun(X5014,bool),bool),member(X5014),esk79_5(X5013,X5014,X5015,X5016,X5017)),X5017)) )
      & ( ~ hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5015),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5016),X5017))
        | hAPP(X5014,X5013,X5015,esk79_5(X5013,X5014,X5015,X5016,X5017)) != hAPP(X5014,X5013,X5016,esk79_5(X5013,X5014,X5015,X5016,X5017)) )
      & ( ~ hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5016),X5017))
        | hBOOL(hAPP(fun(X5014,bool),bool,hAPP(fun(X5014,X5013),fun(fun(X5014,bool),bool),inj_on(X5014,X5013),X5015),X5017))
        | hAPP(X5014,X5013,X5015,esk79_5(X5013,X5014,X5015,X5016,X5017)) != hAPP(X5014,X5013,X5016,esk79_5(X5013,X5014,X5015,X5016,X5017)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_318_inj__on__cong])])])]) ).

cnf(i_0_1830,plain,
    ( ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X3)
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2)))
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1211]) ).

cnf(i_0_1831,plain,
    ( ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X1)
    | ti(arrow_2142409994le_alt,X3) = ti(arrow_2142409994le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2)))
    | ti(arrow_2142409994le_alt,X1) != ti(arrow_2142409994le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1212]) ).

fof(i_0_1832,plain,
    ! [X7381,X7382,X7383,X7384] :
      ( ~ comm_monoid_add(X7381)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X7383),X7384))
      | hAPP(fun(nat,bool),X7381,hAPP(fun(nat,X7381),fun(fun(nat,bool),X7381),big_co1399186613setsum(nat,X7381),X7382),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7383),X7384)) = hAPP(X7381,X7381,hAPP(X7381,fun(X7381,X7381),plus_plus(X7381),hAPP(nat,X7381,X7382,X7383)),hAPP(fun(nat,bool),X7381,hAPP(fun(nat,X7381),fun(fun(nat,bool),X7381),big_co1399186613setsum(nat,X7381),X7382),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X7383)),X7384))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_960_setsum__head__upt__Suc])])]) ).

fof(i_0_1833,plain,
    ! [X7385,X7386,X7387,X7388] :
      ( ~ comm_monoid_add(X7385)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7387),X7388))
      | hAPP(fun(nat,bool),X7385,hAPP(fun(nat,X7385),fun(fun(nat,bool),X7385),big_co1399186613setsum(nat,X7385),X7386),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7387),X7388)) = hAPP(X7385,X7385,hAPP(X7385,fun(X7385,X7385),plus_plus(X7385),hAPP(nat,X7385,X7386,X7387)),hAPP(fun(nat,bool),X7385,hAPP(fun(nat,X7385),fun(fun(nat,bool),X7385),big_co1399186613setsum(nat,X7385),X7386),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X7387)),X7388))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_961_setsum__head__Suc])])]) ).

fof(i_0_1834,plain,
    ! [X4024,X4025,X4026,X4027,X4028] :
      ( ( ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4024),X4025))
        | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4026),arrow_301600364e_Prof))
        | hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4024,X4026) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4026,X4025) )
      & ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk18_2(X4027,X4028)),arrow_301600364e_Prof))
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4027),X4028)) )
      & ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4027,esk18_2(X4027,X4028)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk18_2(X4027,X4028),X4028)
        | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X4027),X4028)) ) ),
    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_34_dictator__def])])])])])]) ).

fof(i_0_1835,plain,
    ! [X6028,X6029,X6030,X6031] :
      ( ~ ordered_semiring(X6028)
      | ~ hBOOL(hAPP(X6028,bool,hAPP(X6028,fun(X6028,bool),ord_less_eq(X6028),X6030),X6031))
      | ~ hBOOL(hAPP(X6028,bool,hAPP(X6028,fun(X6028,bool),ord_less_eq(X6028),zero_zero(X6028)),X6029))
      | hBOOL(hAPP(X6028,bool,hAPP(X6028,fun(X6028,bool),ord_less_eq(X6028),hAPP(X6028,X6028,hAPP(X6028,fun(X6028,X6028),times_times(X6028),X6030),X6029)),hAPP(X6028,X6028,hAPP(X6028,fun(X6028,X6028),times_times(X6028),X6031),X6029))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_627_mult__right__mono])])]) ).

fof(i_0_1836,plain,
    ! [X6036,X6037,X6038,X6039] :
      ( ~ ordere1490568538miring(X6036)
      | ~ hBOOL(hAPP(X6036,bool,hAPP(X6036,fun(X6036,bool),ord_less_eq(X6036),X6038),X6039))
      | ~ hBOOL(hAPP(X6036,bool,hAPP(X6036,fun(X6036,bool),ord_less_eq(X6036),zero_zero(X6036)),X6037))
      | hBOOL(hAPP(X6036,bool,hAPP(X6036,fun(X6036,bool),ord_less_eq(X6036),hAPP(X6036,X6036,hAPP(X6036,fun(X6036,X6036),times_times(X6036),X6037),X6038)),hAPP(X6036,X6036,hAPP(X6036,fun(X6036,X6036),times_times(X6036),X6037),X6039))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_629_comm__mult__left__mono])])]) ).

fof(i_0_1837,plain,
    ! [X6032,X6033,X6034,X6035] :
      ( ~ ordered_semiring(X6032)
      | ~ hBOOL(hAPP(X6032,bool,hAPP(X6032,fun(X6032,bool),ord_less_eq(X6032),X6034),X6035))
      | ~ hBOOL(hAPP(X6032,bool,hAPP(X6032,fun(X6032,bool),ord_less_eq(X6032),zero_zero(X6032)),X6033))
      | hBOOL(hAPP(X6032,bool,hAPP(X6032,fun(X6032,bool),ord_less_eq(X6032),hAPP(X6032,X6032,hAPP(X6032,fun(X6032,X6032),times_times(X6032),X6033),X6034)),hAPP(X6032,X6032,hAPP(X6032,fun(X6032,X6032),times_times(X6032),X6033),X6035))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_628_mult__left__mono])])]) ).

fof(i_0_1838,plain,
    ! [X6103,X6104,X6105,X6106] :
      ( ~ linord20386208strict(X6103)
      | ~ hBOOL(hAPP(X6103,bool,hAPP(X6103,fun(X6103,bool),ord_less(X6103),X6105),X6106))
      | ~ hBOOL(hAPP(X6103,bool,hAPP(X6103,fun(X6103,bool),ord_less(X6103),zero_zero(X6103)),X6104))
      | hBOOL(hAPP(X6103,bool,hAPP(X6103,fun(X6103,bool),ord_less(X6103),hAPP(X6103,X6103,hAPP(X6103,fun(X6103,X6103),times_times(X6103),X6105),X6104)),hAPP(X6103,X6103,hAPP(X6103,fun(X6103,X6103),times_times(X6103),X6106),X6104))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_648_mult__strict__right__mono])])]) ).

fof(i_0_1839,plain,
    ! [X6111,X6112,X6113,X6114] :
      ( ~ linord893533164strict(X6111)
      | ~ hBOOL(hAPP(X6111,bool,hAPP(X6111,fun(X6111,bool),ord_less(X6111),X6113),X6114))
      | ~ hBOOL(hAPP(X6111,bool,hAPP(X6111,fun(X6111,bool),ord_less(X6111),zero_zero(X6111)),X6112))
      | hBOOL(hAPP(X6111,bool,hAPP(X6111,fun(X6111,bool),ord_less(X6111),hAPP(X6111,X6111,hAPP(X6111,fun(X6111,X6111),times_times(X6111),X6112),X6113)),hAPP(X6111,X6111,hAPP(X6111,fun(X6111,X6111),times_times(X6111),X6112),X6114))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_650_comm__mult__strict__left__mono])])]) ).

fof(i_0_1840,plain,
    ! [X6107,X6108,X6109,X6110] :
      ( ~ linord20386208strict(X6107)
      | ~ hBOOL(hAPP(X6107,bool,hAPP(X6107,fun(X6107,bool),ord_less(X6107),X6109),X6110))
      | ~ hBOOL(hAPP(X6107,bool,hAPP(X6107,fun(X6107,bool),ord_less(X6107),zero_zero(X6107)),X6108))
      | hBOOL(hAPP(X6107,bool,hAPP(X6107,fun(X6107,bool),ord_less(X6107),hAPP(X6107,X6107,hAPP(X6107,fun(X6107,X6107),times_times(X6107),X6108),X6109)),hAPP(X6107,X6107,hAPP(X6107,fun(X6107,X6107),times_times(X6107),X6108),X6110))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_649_mult__strict__left__mono])])]) ).

fof(i_0_1841,plain,
    ! [X6040,X6041,X6042,X6043] :
      ( ~ ordered_ring(X6040)
      | ~ hBOOL(hAPP(X6040,bool,hAPP(X6040,fun(X6040,bool),ord_less_eq(X6040),X6042),X6043))
      | ~ hBOOL(hAPP(X6040,bool,hAPP(X6040,fun(X6040,bool),ord_less_eq(X6040),X6041),zero_zero(X6040)))
      | hBOOL(hAPP(X6040,bool,hAPP(X6040,fun(X6040,bool),ord_less_eq(X6040),hAPP(X6040,X6040,hAPP(X6040,fun(X6040,X6040),times_times(X6040),X6043),X6041)),hAPP(X6040,X6040,hAPP(X6040,fun(X6040,X6040),times_times(X6040),X6042),X6041))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_630_mult__right__mono__neg])])]) ).

fof(i_0_1842,plain,
    ! [X6044,X6045,X6046,X6047] :
      ( ~ ordered_ring(X6044)
      | ~ hBOOL(hAPP(X6044,bool,hAPP(X6044,fun(X6044,bool),ord_less_eq(X6044),X6046),X6047))
      | ~ hBOOL(hAPP(X6044,bool,hAPP(X6044,fun(X6044,bool),ord_less_eq(X6044),X6045),zero_zero(X6044)))
      | hBOOL(hAPP(X6044,bool,hAPP(X6044,fun(X6044,bool),ord_less_eq(X6044),hAPP(X6044,X6044,hAPP(X6044,fun(X6044,X6044),times_times(X6044),X6045),X6047)),hAPP(X6044,X6044,hAPP(X6044,fun(X6044,X6044),times_times(X6044),X6045),X6046))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_631_mult__left__mono__neg])])]) ).

fof(i_0_1843,plain,
    ! [X6115,X6116,X6117,X6118] :
      ( ~ linord581940658strict(X6115)
      | ~ hBOOL(hAPP(X6115,bool,hAPP(X6115,fun(X6115,bool),ord_less(X6115),X6117),X6118))
      | ~ hBOOL(hAPP(X6115,bool,hAPP(X6115,fun(X6115,bool),ord_less(X6115),X6116),zero_zero(X6115)))
      | hBOOL(hAPP(X6115,bool,hAPP(X6115,fun(X6115,bool),ord_less(X6115),hAPP(X6115,X6115,hAPP(X6115,fun(X6115,X6115),times_times(X6115),X6118),X6116)),hAPP(X6115,X6115,hAPP(X6115,fun(X6115,X6115),times_times(X6115),X6117),X6116))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_651_mult__strict__right__mono__neg])])]) ).

fof(i_0_1844,plain,
    ! [X6119,X6120,X6121,X6122] :
      ( ~ linord581940658strict(X6119)
      | ~ hBOOL(hAPP(X6119,bool,hAPP(X6119,fun(X6119,bool),ord_less(X6119),X6121),X6122))
      | ~ hBOOL(hAPP(X6119,bool,hAPP(X6119,fun(X6119,bool),ord_less(X6119),X6120),zero_zero(X6119)))
      | hBOOL(hAPP(X6119,bool,hAPP(X6119,fun(X6119,bool),ord_less(X6119),hAPP(X6119,X6119,hAPP(X6119,fun(X6119,X6119),times_times(X6119),X6120),X6122)),hAPP(X6119,X6119,hAPP(X6119,fun(X6119,X6119),times_times(X6119),X6120),X6121))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_652_mult__strict__left__mono__neg])])]) ).

fof(i_0_1845,plain,
    ! [X6960,X6961,X6962,X6963,X6964] :
      ( ~ semilattice_sup(X6960)
      | ~ hBOOL(hAPP(X6960,bool,hAPP(X6960,fun(X6960,bool),ord_less_eq(X6960),X6963),X6964))
      | ~ hBOOL(hAPP(X6960,bool,hAPP(X6960,fun(X6960,bool),ord_less_eq(X6960),X6961),X6962))
      | hBOOL(hAPP(X6960,bool,hAPP(X6960,fun(X6960,bool),ord_less_eq(X6960),hAPP(X6960,X6960,hAPP(X6960,fun(X6960,X6960),semilattice_sup_sup(X6960),X6963),X6961)),hAPP(X6960,X6960,hAPP(X6960,fun(X6960,X6960),semilattice_sup_sup(X6960),X6964),X6962))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_848_sup__mono])])]) ).

fof(i_0_1846,plain,
    ! [X7243,X7244,X7245,X7246,X7247] :
      ( ~ semilattice_inf(X7243)
      | ~ hBOOL(hAPP(X7243,bool,hAPP(X7243,fun(X7243,bool),ord_less_eq(X7243),X7246),X7247))
      | ~ hBOOL(hAPP(X7243,bool,hAPP(X7243,fun(X7243,bool),ord_less_eq(X7243),X7244),X7245))
      | hBOOL(hAPP(X7243,bool,hAPP(X7243,fun(X7243,bool),ord_less_eq(X7243),hAPP(X7243,X7243,hAPP(X7243,fun(X7243,X7243),semilattice_inf_inf(X7243),X7246),X7244)),hAPP(X7243,X7243,hAPP(X7243,fun(X7243,X7243),semilattice_inf_inf(X7243),X7247),X7245))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_921_inf__mono])])]) ).

fof(i_0_1847,plain,
    ! [X4509,X4510,X4511,X4512,X4513] :
      ( ~ ordere779506340up_add(X4509)
      | ~ hBOOL(hAPP(X4509,bool,hAPP(X4509,fun(X4509,bool),ord_less_eq(X4509),X4512),X4513))
      | ~ hBOOL(hAPP(X4509,bool,hAPP(X4509,fun(X4509,bool),ord_less_eq(X4509),X4510),X4511))
      | hBOOL(hAPP(X4509,bool,hAPP(X4509,fun(X4509,bool),ord_less_eq(X4509),hAPP(X4509,X4509,hAPP(X4509,fun(X4509,X4509),plus_plus(X4509),X4512),X4510)),hAPP(X4509,X4509,hAPP(X4509,fun(X4509,X4509),plus_plus(X4509),X4513),X4511))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_add__mono])])]) ).

fof(i_0_1848,plain,
    ! [X4412,X4413,X4414,X4415,X4416] :
      ( ~ ordere223160158up_add(X4412)
      | ~ hBOOL(hAPP(X4412,bool,hAPP(X4412,fun(X4412,bool),ord_less(X4412),X4415),X4416))
      | ~ hBOOL(hAPP(X4412,bool,hAPP(X4412,fun(X4412,bool),ord_less_eq(X4412),X4413),X4414))
      | hBOOL(hAPP(X4412,bool,hAPP(X4412,fun(X4412,bool),ord_less(X4412),hAPP(X4412,X4412,hAPP(X4412,fun(X4412,X4412),plus_plus(X4412),X4415),X4413)),hAPP(X4412,X4412,hAPP(X4412,fun(X4412,X4412),plus_plus(X4412),X4416),X4414))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_add__less__le__mono])])]) ).

fof(i_0_1849,plain,
    ! [X4417,X4418,X4419,X4420,X4421] :
      ( ~ ordere223160158up_add(X4417)
      | ~ hBOOL(hAPP(X4417,bool,hAPP(X4417,fun(X4417,bool),ord_less_eq(X4417),X4420),X4421))
      | ~ hBOOL(hAPP(X4417,bool,hAPP(X4417,fun(X4417,bool),ord_less(X4417),X4418),X4419))
      | hBOOL(hAPP(X4417,bool,hAPP(X4417,fun(X4417,bool),ord_less(X4417),hAPP(X4417,X4417,hAPP(X4417,fun(X4417,X4417),plus_plus(X4417),X4420),X4418)),hAPP(X4417,X4417,hAPP(X4417,fun(X4417,X4417),plus_plus(X4417),X4421),X4419))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_add__le__less__mono])])]) ).

fof(i_0_1850,plain,
    ! [X4538,X4539,X4540,X4541,X4542] :
      ( ~ ordere223160158up_add(X4538)
      | ~ hBOOL(hAPP(X4538,bool,hAPP(X4538,fun(X4538,bool),ord_less(X4538),X4541),X4542))
      | ~ hBOOL(hAPP(X4538,bool,hAPP(X4538,fun(X4538,bool),ord_less(X4538),X4539),X4540))
      | hBOOL(hAPP(X4538,bool,hAPP(X4538,fun(X4538,bool),ord_less(X4538),hAPP(X4538,X4538,hAPP(X4538,fun(X4538,X4538),plus_plus(X4538),X4541),X4539)),hAPP(X4538,X4538,hAPP(X4538,fun(X4538,X4538),plus_plus(X4538),X4542),X4540))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_add__strict__mono])])]) ).

fof(i_0_1851,plain,
    ! [X4821,X4822,X4823] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X4821,X4822,X4823)),esk64_3(X4821,X4822,X4823)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4821),X4822))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X4823,X4821)),hAPP(nat,nat,X4823,X4822))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X4823,esk63_3(X4821,X4822,X4823))),hAPP(nat,nat,X4823,esk64_3(X4821,X4822,X4823))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4821),X4822))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X4823,X4821)),hAPP(nat,nat,X4823,X4822))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_less__mono__imp__le__mono])])])]) ).

fof(i_0_1852,plain,
    ! [X6010,X6011,X6012] :
      ( ( hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6011),zero_zero(X6010)))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6011))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) )
      & ( hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6012))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6011))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) )
      & ( hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6011),zero_zero(X6010)))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6012),zero_zero(X6010)))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) )
      & ( hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6012))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6012),zero_zero(X6010)))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) )
      & ( ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6011))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6012),zero_zero(X6010)))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) )
      & ( ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),X6011),zero_zero(X6010)))
        | ~ hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),zero_zero(X6010)),X6012))
        | hBOOL(hAPP(X6010,bool,hAPP(X6010,fun(X6010,bool),ord_less_eq(X6010),hAPP(X6010,X6010,hAPP(X6010,fun(X6010,X6010),times_times(X6010),X6011),X6012)),zero_zero(X6010)))
        | ~ linord581940658strict(X6010) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_621_mult__le__0__iff])])])]) ).

fof(i_0_1853,plain,
    ! [X6148,X6149,X6150] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6149),X6150))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6148))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6149),X6148)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6150),X6148))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_661_mult__less__mono1])]) ).

fof(i_0_1854,plain,
    ! [X6145,X6146,X6147] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6146),X6147))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6145))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6145),X6146)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6145),X6147))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_660_mult__less__mono2])]) ).

fof(i_0_1855,plain,
    ! [X5873,X5874,X5875,X5876] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5875),X5876))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5873),X5874))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5875),X5873)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5876),X5874))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_576_mult__le__mono])]) ).

fof(i_0_1856,plain,
    ! [X4790,X4791,X4792,X4793] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4792),X4793))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4790),X4791))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4792),X4790)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4793),X4791))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_add__le__mono])]) ).

fof(i_0_1857,plain,
    ! [X4747,X4748,X4749,X4750] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4749),X4750))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4747),X4748))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4749),X4747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4750),X4748))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_add__less__mono])]) ).

fof(i_0_1858,plain,
    ! [X7147,X7148,X7149,X7150] :
      ( ( hBOOL(hAPP(fun(X7147,bool),bool,hAPP(X7147,fun(fun(X7147,bool),bool),member(X7147),X7148),X7149))
        | ~ hBOOL(hAPP(fun(X7147,bool),bool,hAPP(X7147,fun(fun(X7147,bool),bool),member(X7147),X7148),hAPP(fun(X7147,bool),fun(X7147,bool),hAPP(fun(X7147,bool),fun(fun(X7147,bool),fun(X7147,bool)),semilattice_inf_inf(fun(X7147,bool)),X7149),hAPP(fun(X7147,bool),fun(X7147,bool),collect(X7147),X7150)))) )
      & ( hBOOL(hAPP(X7147,bool,X7150,X7148))
        | ~ hBOOL(hAPP(fun(X7147,bool),bool,hAPP(X7147,fun(fun(X7147,bool),bool),member(X7147),X7148),hAPP(fun(X7147,bool),fun(X7147,bool),hAPP(fun(X7147,bool),fun(fun(X7147,bool),fun(X7147,bool)),semilattice_inf_inf(fun(X7147,bool)),X7149),hAPP(fun(X7147,bool),fun(X7147,bool),collect(X7147),X7150)))) )
      & ( ~ hBOOL(hAPP(fun(X7147,bool),bool,hAPP(X7147,fun(fun(X7147,bool),bool),member(X7147),X7148),X7149))
        | ~ hBOOL(hAPP(X7147,bool,X7150,X7148))
        | hBOOL(hAPP(fun(X7147,bool),bool,hAPP(X7147,fun(fun(X7147,bool),bool),member(X7147),X7148),hAPP(fun(X7147,bool),fun(X7147,bool),hAPP(fun(X7147,bool),fun(fun(X7147,bool),fun(X7147,bool)),semilattice_inf_inf(fun(X7147,bool)),X7149),hAPP(fun(X7147,bool),fun(X7147,bool),collect(X7147),X7150)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_896_Int__Collect])])]) ).

fof(i_0_1859,plain,
    ! [X6257,X6258] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6258))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6257))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6258),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6258),X6257))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_692_n__less__n__mult__m])]) ).

fof(i_0_1860,plain,
    ! [X6255,X6256] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6256))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X6255))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6256),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6255),X6256))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_691_n__less__m__mult__n])]) ).

fof(i_0_1861,plain,
    ! [X6252,X6253,X6254] :
      ( ~ linordered_idom(X6252)
      | ~ hBOOL(hAPP(X6252,bool,hAPP(X6252,fun(X6252,bool),ord_less_eq(X6252),zero_zero(X6252)),X6254))
      | ~ hBOOL(hAPP(X6252,bool,hAPP(X6252,fun(X6252,bool),ord_less_eq(X6252),zero_zero(X6252)),X6253))
      | ~ hBOOL(hAPP(X6252,bool,hAPP(X6252,fun(X6252,bool),ord_less_eq(X6252),X6253),one_one(X6252)))
      | hBOOL(hAPP(X6252,bool,hAPP(X6252,fun(X6252,bool),ord_less_eq(X6252),hAPP(X6252,X6252,hAPP(X6252,fun(X6252,X6252),times_times(X6252),X6254),X6253)),X6254)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_690_mult__right__le__one__le])])]) ).

fof(i_0_1862,plain,
    ! [X6249,X6250,X6251] :
      ( ~ linordered_idom(X6249)
      | ~ hBOOL(hAPP(X6249,bool,hAPP(X6249,fun(X6249,bool),ord_less_eq(X6249),zero_zero(X6249)),X6251))
      | ~ hBOOL(hAPP(X6249,bool,hAPP(X6249,fun(X6249,bool),ord_less_eq(X6249),zero_zero(X6249)),X6250))
      | ~ hBOOL(hAPP(X6249,bool,hAPP(X6249,fun(X6249,bool),ord_less_eq(X6249),X6250),one_one(X6249)))
      | hBOOL(hAPP(X6249,bool,hAPP(X6249,fun(X6249,bool),ord_less_eq(X6249),hAPP(X6249,X6249,hAPP(X6249,fun(X6249,X6249),times_times(X6249),X6250),X6251)),X6251)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_689_mult__left__le__one__le])])]) ).

cnf(i_0_1863,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_1232]) ).

cnf(i_0_1864,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_1233]) ).

fof(i_0_1865,plain,
    ! [X6566,X6569] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X6566,hAPP(nat,nat,suc,esk153_1(X6566)))),hAPP(nat,nat,X6566,esk153_1(X6566))))
      | hAPP(nat,nat,X6566,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk154_1(X6566)),X6569)) = hAPP(nat,nat,X6566,esk154_1(X6566)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_752_weak__decr__stable])])])]) ).

cnf(i_0_1866,plain,
    ( ti(X3,X5) = ti(X3,esk104_4(X3,X1,X2,X4))
    | ti(X1,X2) != hAPP(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),top_top(fun(X3,bool)))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]) ).

fof(i_0_1867,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    inference(fof_simplification,[status(thm)],[fact_41__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).

fof(i_0_1868,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    inference(fof_simplification,[status(thm)],[fact_40__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).

cnf(i_0_1869,plain,
    ( 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),top_top(fun(X1,bool)))))
    | ti(X1,esk105_5(X1,X2,X3,X4,X5)) != ti(X1,X5)
    | ti(X2,X3) != hAPP(X1,X2,X4,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]) ).

cnf(i_0_1870,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),esk111_5(X3,X1,X4,X5,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(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,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1235]) ).

cnf(i_0_1871,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X5))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk69_5(X1,X2,X3,X4,X5))) != ti(X2,esk69_5(X1,X2,X3,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1236]) ).

cnf(i_0_1872,plain,
    ( 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),X4),X3)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)) = ti(fun(X1,bool),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_1237]) ).

cnf(i_0_1873,plain,
    ( ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5)
    | 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),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_1238]) ).

fof(i_0_1874,plain,
    ! [X7373,X7374,X7375,X7376,X7377] :
      ( ~ hBOOL(hAPP(fun(X7373,bool),bool,hAPP(fun(X7373,X7374),fun(fun(X7373,bool),bool),inj_on(X7373,X7374),X7377),top_top(fun(X7373,bool))))
      | hAPP(fun(X7373,bool),fun(X7374,bool),hAPP(fun(X7373,X7374),fun(fun(X7373,bool),fun(X7374,bool)),image(X7373,X7374),X7377),hAPP(fun(X7373,bool),fun(X7373,bool),hAPP(fun(X7373,bool),fun(fun(X7373,bool),fun(X7373,bool)),semilattice_inf_inf(fun(X7373,bool)),X7375),X7376)) = hAPP(fun(X7374,bool),fun(X7374,bool),hAPP(fun(X7374,bool),fun(fun(X7374,bool),fun(X7374,bool)),semilattice_inf_inf(fun(X7374,bool)),hAPP(fun(X7373,bool),fun(X7374,bool),hAPP(fun(X7373,X7374),fun(fun(X7373,bool),fun(X7374,bool)),image(X7373,X7374),X7377),X7375)),hAPP(fun(X7373,bool),fun(X7374,bool),hAPP(fun(X7373,X7374),fun(fun(X7373,bool),fun(X7374,bool)),image(X7373,X7374),X7377),X7376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_958_image__Int])]) ).

fof(i_0_1875,plain,
    ! [X6548,X6549,X6550,X6551,X6552,X6553,X6554] :
      ( ~ hBOOL(hAPP(fun(fun(X6549,bool),fun(X6550,X6550)),bool,hAPP(fun(X6549,fun(X6550,X6550)),fun(fun(fun(X6549,bool),fun(X6550,X6550)),bool),finite_folding_idem(X6549,X6550),X6553),X6554))
      | hAPP(fun(X6548,X6550),fun(X6548,X6550),hAPP(fun(X6550,X6550),fun(fun(X6548,X6550),fun(X6548,X6550)),comp(X6550,X6550,X6548),hAPP(X6549,fun(X6550,X6550),X6553,X6551)),hAPP(fun(X6548,X6550),fun(X6548,X6550),hAPP(fun(X6550,X6550),fun(fun(X6548,X6550),fun(X6548,X6550)),comp(X6550,X6550,X6548),hAPP(X6549,fun(X6550,X6550),X6553,X6551)),X6552)) = hAPP(fun(X6548,X6550),fun(X6548,X6550),hAPP(fun(X6550,X6550),fun(fun(X6548,X6550),fun(X6548,X6550)),comp(X6550,X6550,X6548),hAPP(X6549,fun(X6550,X6550),X6553,X6551)),X6552) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_749_folding__idem_Oidem__left__comp])]) ).

cnf(i_0_1876,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk104_4(X3,X1,X2,X4))
    | ~ 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)))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]) ).

fof(i_0_1877,plain,
    ! [X5927,X5928,X5929,X5930,X5931] :
      ( ~ comm_semiring_1(X5927)
      | hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),X5928),X5929)),hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),X5930),X5931)) = hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),X5930),hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),hAPP(X5927,X5927,hAPP(X5927,fun(X5927,X5927),times_times(X5927),X5928),X5929)),X5931)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])])]) ).

fof(i_0_1878,plain,
    ! [X6826,X6827,X6828] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6827),X6828))
      | hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X6827),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6828),X6826)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X6827),X6828)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X6828),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6828),X6826))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_810_atLeastLessThan__add__Un])]) ).

fof(i_0_1879,plain,
    ! [X5066,X5067] :
      ( ( ~ hBOOL(hAPP(X5066,bool,hAPP(X5066,fun(X5066,bool),ord_less_eq(X5066),hAPP(X5066,X5066,hAPP(X5066,fun(X5066,X5066),plus_plus(X5066),X5067),X5067)),zero_zero(X5066)))
        | hBOOL(hAPP(X5066,bool,hAPP(X5066,fun(X5066,bool),ord_less_eq(X5066),X5067),zero_zero(X5066)))
        | ~ linord219039673up_add(X5066) )
      & ( ~ hBOOL(hAPP(X5066,bool,hAPP(X5066,fun(X5066,bool),ord_less_eq(X5066),X5067),zero_zero(X5066)))
        | hBOOL(hAPP(X5066,bool,hAPP(X5066,fun(X5066,bool),ord_less_eq(X5066),hAPP(X5066,X5066,hAPP(X5066,fun(X5066,X5066),plus_plus(X5066),X5067),X5067)),zero_zero(X5066)))
        | ~ linord219039673up_add(X5066) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_double__add__le__zero__iff__single__add__le__zero])])])]) ).

fof(i_0_1880,plain,
    ! [X5080,X5081] :
      ( ( ~ hBOOL(hAPP(X5080,bool,hAPP(X5080,fun(X5080,bool),ord_less(X5080),hAPP(X5080,X5080,hAPP(X5080,fun(X5080,X5080),plus_plus(X5080),X5081),X5081)),zero_zero(X5080)))
        | hBOOL(hAPP(X5080,bool,hAPP(X5080,fun(X5080,bool),ord_less(X5080),X5081),zero_zero(X5080)))
        | ~ linord219039673up_add(X5080) )
      & ( ~ hBOOL(hAPP(X5080,bool,hAPP(X5080,fun(X5080,bool),ord_less(X5080),X5081),zero_zero(X5080)))
        | hBOOL(hAPP(X5080,bool,hAPP(X5080,fun(X5080,bool),ord_less(X5080),hAPP(X5080,X5080,hAPP(X5080,fun(X5080,X5080),plus_plus(X5080),X5081),X5081)),zero_zero(X5080)))
        | ~ linord219039673up_add(X5080) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_double__add__less__zero__iff__single__add__less__zero])])])]) ).

fof(i_0_1881,plain,
    ! [X5130,X5131] :
      ( ( ~ hBOOL(hAPP(X5130,bool,hAPP(X5130,fun(X5130,bool),ord_less(X5130),hAPP(X5130,X5130,hAPP(X5130,fun(X5130,X5130),plus_plus(X5130),X5131),X5131)),zero_zero(X5130)))
        | hBOOL(hAPP(X5130,bool,hAPP(X5130,fun(X5130,bool),ord_less(X5130),X5131),zero_zero(X5130)))
        | ~ linordered_idom(X5130) )
      & ( ~ hBOOL(hAPP(X5130,bool,hAPP(X5130,fun(X5130,bool),ord_less(X5130),X5131),zero_zero(X5130)))
        | hBOOL(hAPP(X5130,bool,hAPP(X5130,fun(X5130,bool),ord_less(X5130),hAPP(X5130,X5130,hAPP(X5130,fun(X5130,X5130),plus_plus(X5130),X5131),X5131)),zero_zero(X5130)))
        | ~ linordered_idom(X5130) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_371_even__less__0__iff])])])]) ).

cnf(i_0_1882,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_1239]) ).

fof(i_0_1883,plain,
    ! [X6965,X6966,X6967,X6968] :
      ( ( hBOOL(hAPP(X6965,bool,hAPP(X6965,fun(X6965,bool),ord_less_eq(X6965),X6966),X6968))
        | ~ hBOOL(hAPP(X6965,bool,hAPP(X6965,fun(X6965,bool),ord_less_eq(X6965),hAPP(X6965,X6965,hAPP(X6965,fun(X6965,X6965),semilattice_sup_sup(X6965),X6966),X6967)),X6968))
        | ~ semilattice_sup(X6965) )
      & ( hBOOL(hAPP(X6965,bool,hAPP(X6965,fun(X6965,bool),ord_less_eq(X6965),X6967),X6968))
        | ~ hBOOL(hAPP(X6965,bool,hAPP(X6965,fun(X6965,bool),ord_less_eq(X6965),hAPP(X6965,X6965,hAPP(X6965,fun(X6965,X6965),semilattice_sup_sup(X6965),X6966),X6967)),X6968))
        | ~ semilattice_sup(X6965) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1240])])])]) ).

fof(i_0_1884,plain,
    ! [X6934,X6935,X6936,X6937] :
      ( ( hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),X6935),X6937))
        | ~ hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),hAPP(X6934,X6934,hAPP(X6934,fun(X6934,X6934),semilattice_sup_sup(X6934),X6935),X6936)),X6937))
        | ~ semilattice_sup(X6934) )
      & ( hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),X6936),X6937))
        | ~ hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),hAPP(X6934,X6934,hAPP(X6934,fun(X6934,X6934),semilattice_sup_sup(X6934),X6935),X6936)),X6937))
        | ~ semilattice_sup(X6934) )
      & ( ~ hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),X6935),X6937))
        | ~ hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),X6936),X6937))
        | hBOOL(hAPP(X6934,bool,hAPP(X6934,fun(X6934,bool),ord_less_eq(X6934),hAPP(X6934,X6934,hAPP(X6934,fun(X6934,X6934),semilattice_sup_sup(X6934),X6935),X6936)),X6937))
        | ~ semilattice_sup(X6934) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_841_le__sup__iff])])])]) ).

fof(i_0_1885,plain,
    ! [X5862,X5863,X5864] :
      ( ~ ring_1(X5862)
      | ~ hBOOL(hAPP(fun(X5862,bool),bool,hAPP(X5862,fun(fun(X5862,bool),bool),member(X5862),X5864),ring_1_Ints(X5862)))
      | ~ hBOOL(hAPP(fun(X5862,bool),bool,hAPP(X5862,fun(fun(X5862,bool),bool),member(X5862),X5863),ring_1_Ints(X5862)))
      | hBOOL(hAPP(fun(X5862,bool),bool,hAPP(X5862,fun(fun(X5862,bool),bool),member(X5862),hAPP(X5862,X5862,hAPP(X5862,fun(X5862,X5862),times_times(X5862),X5864),X5863)),ring_1_Ints(X5862))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_571_Ints__mult])])]) ).

fof(i_0_1886,plain,
    ! [X5699,X5700,X5701] :
      ( ~ ring_1(X5699)
      | ~ hBOOL(hAPP(fun(X5699,bool),bool,hAPP(X5699,fun(fun(X5699,bool),bool),member(X5699),X5701),ring_1_Ints(X5699)))
      | ~ hBOOL(hAPP(fun(X5699,bool),bool,hAPP(X5699,fun(fun(X5699,bool),bool),member(X5699),X5700),ring_1_Ints(X5699)))
      | hBOOL(hAPP(fun(X5699,bool),bool,hAPP(X5699,fun(fun(X5699,bool),bool),member(X5699),hAPP(X5699,X5699,hAPP(X5699,fun(X5699,X5699),plus_plus(X5699),X5701),X5700)),ring_1_Ints(X5699))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_536_Ints__add])])]) ).

fof(i_0_1887,plain,
    ! [X7099,X7100,X7101,X7102] : hAPP(fun(X7099,bool),fun(X7099,bool),hAPP(fun(X7099,bool),fun(fun(X7099,bool),fun(X7099,bool)),semilattice_sup_sup(fun(X7099,bool)),hAPP(fun(X7099,bool),fun(X7099,bool),hAPP(fun(X7099,bool),fun(fun(X7099,bool),fun(X7099,bool)),semilattice_inf_inf(fun(X7099,bool)),X7100),X7101)),X7102) = hAPP(fun(X7099,bool),fun(X7099,bool),hAPP(fun(X7099,bool),fun(fun(X7099,bool),fun(X7099,bool)),semilattice_inf_inf(fun(X7099,bool)),hAPP(fun(X7099,bool),fun(X7099,bool),hAPP(fun(X7099,bool),fun(fun(X7099,bool),fun(X7099,bool)),semilattice_sup_sup(fun(X7099,bool)),X7100),X7102)),hAPP(fun(X7099,bool),fun(X7099,bool),hAPP(fun(X7099,bool),fun(fun(X7099,bool),fun(X7099,bool)),semilattice_sup_sup(fun(X7099,bool)),X7101),X7102)),
    inference(variable_rename,[status(thm)],[fact_885_Un__Int__distrib2]) ).

fof(i_0_1888,plain,
    ! [X7095,X7096,X7097,X7098] : hAPP(fun(X7095,bool),fun(X7095,bool),hAPP(fun(X7095,bool),fun(fun(X7095,bool),fun(X7095,bool)),semilattice_inf_inf(fun(X7095,bool)),hAPP(fun(X7095,bool),fun(X7095,bool),hAPP(fun(X7095,bool),fun(fun(X7095,bool),fun(X7095,bool)),semilattice_sup_sup(fun(X7095,bool)),X7096),X7097)),X7098) = hAPP(fun(X7095,bool),fun(X7095,bool),hAPP(fun(X7095,bool),fun(fun(X7095,bool),fun(X7095,bool)),semilattice_sup_sup(fun(X7095,bool)),hAPP(fun(X7095,bool),fun(X7095,bool),hAPP(fun(X7095,bool),fun(fun(X7095,bool),fun(X7095,bool)),semilattice_inf_inf(fun(X7095,bool)),X7096),X7098)),hAPP(fun(X7095,bool),fun(X7095,bool),hAPP(fun(X7095,bool),fun(fun(X7095,bool),fun(X7095,bool)),semilattice_inf_inf(fun(X7095,bool)),X7097),X7098)),
    inference(variable_rename,[status(thm)],[fact_884_Int__Un__distrib2]) ).

fof(i_0_1889,plain,
    ! [X5548,X5549,X5550] :
      ( hAPP(fun(X5548,bool),fun(X5549,bool),hAPP(fun(X5548,X5549),fun(fun(X5548,bool),fun(X5549,bool)),image(X5548,X5549),X5550),top_top(fun(X5548,bool))) != top_top(fun(X5549,bool))
      | hBOOL(hAPP(fun(X5549,bool),bool,hAPP(fun(X5549,X5548),fun(fun(X5549,bool),bool),inj_on(X5549,X5548),hAPP(fun(X5548,X5549),fun(X5549,X5548),hAPP(fun(X5548,bool),fun(fun(X5548,X5549),fun(X5549,X5548)),hilbert_inv_into(X5548,X5549),top_top(fun(X5548,bool))),X5550)),top_top(fun(X5549,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_504_surj__imp__inj__inv])]) ).

fof(i_0_1890,plain,
    ! [X6000,X6001,X6002,X6003,X6004] :
      ( ~ hBOOL(hAPP(fun(fun(X6000,X6001),bool),bool,hAPP(fun(X6000,X6001),fun(fun(fun(X6000,X6001),bool),bool),member(fun(X6000,X6001)),X6003),hAPP(fun(X6000,bool),fun(fun(X6000,X6001),bool),extensional(X6000,X6001),X6004)))
      | ~ hBOOL(hAPP(fun(X6000,bool),bool,hAPP(fun(X6000,bool),fun(fun(X6000,bool),bool),ord_less_eq(fun(X6000,bool)),X6004),X6002))
      | hBOOL(hAPP(fun(fun(X6000,X6001),bool),bool,hAPP(fun(X6000,X6001),fun(fun(fun(X6000,X6001),bool),bool),member(fun(X6000,X6001)),X6003),hAPP(fun(X6000,bool),fun(fun(X6000,X6001),bool),extensional(X6000,X6001),X6002))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_618_extensional__subset])]) ).

fof(i_0_1891,plain,
    ! [X4892,X4893,X4894] :
      ( ~ hBOOL(hAPP(fun(X4892,bool),bool,finite_finite_1(X4892),X4894))
      | ~ hBOOL(hAPP(fun(X4892,bool),bool,hAPP(fun(X4892,bool),fun(fun(X4892,bool),bool),ord_less_eq(fun(X4892,bool)),X4893),X4894))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4892,bool),nat,finite_card(X4892),X4893)),hAPP(fun(X4892,bool),nat,finite_card(X4892),X4894)))
      | hBOOL(hAPP(fun(X4892,bool),bool,hAPP(fun(X4892,bool),fun(fun(X4892,bool),bool),ord_less(fun(X4892,bool)),X4893),X4894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_card__psubset])]) ).

fof(i_0_1892,plain,
    ! [X6751,X6752,X6753,X6754] :
      ( ( ~ hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),hAPP(fun(X6751,bool),fun(X6751,bool),hAPP(fun(X6751,bool),fun(fun(X6751,bool),fun(X6751,bool)),semilattice_sup_sup(fun(X6751,bool)),X6753),X6754)))
        | hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),X6753))
        | hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),X6754)) )
      & ( ~ hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),X6753))
        | hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),hAPP(fun(X6751,bool),fun(X6751,bool),hAPP(fun(X6751,bool),fun(fun(X6751,bool),fun(X6751,bool)),semilattice_sup_sup(fun(X6751,bool)),X6753),X6754))) )
      & ( ~ hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),X6754))
        | hBOOL(hAPP(fun(X6751,bool),bool,hAPP(X6751,fun(fun(X6751,bool),bool),member(X6751),X6752),hAPP(fun(X6751,bool),fun(X6751,bool),hAPP(fun(X6751,bool),fun(fun(X6751,bool),fun(X6751,bool)),semilattice_sup_sup(fun(X6751,bool)),X6753),X6754))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_796_Un__iff])])]) ).

fof(i_0_1893,plain,
    ! [X6672,X6673,X6674,X6675] :
      ( ~ hBOOL(hAPP(fun(X6672,bool),bool,hAPP(X6672,fun(fun(X6672,bool),bool),member(X6672),X6673),hAPP(fun(X6672,bool),fun(X6672,bool),hAPP(fun(X6672,bool),fun(fun(X6672,bool),fun(X6672,bool)),semilattice_sup_sup(fun(X6672,bool)),X6674),X6675)))
      | hBOOL(hAPP(fun(X6672,bool),bool,hAPP(X6672,fun(fun(X6672,bool),bool),member(X6672),X6673),X6674))
      | hBOOL(hAPP(fun(X6672,bool),bool,hAPP(X6672,fun(fun(X6672,bool),bool),member(X6672),X6673),X6675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1241])]) ).

fof(i_0_1894,plain,
    ! [X5693,X5694] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5693)),X5694))
        | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5693)),X5694)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5693)),X5694))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5693)),X5694)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_533_less__eq__nat_Osimps_I2_J])]) ).

cnf(i_0_1895,plain,
    ( 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)
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1238]) ).

fof(i_0_1896,plain,
    ! [X4612,X4613,X4614] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4612),X4614))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4612),X4613)),X4614)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4613),X4614))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4612),X4613)),X4614)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1242])])]) ).

fof(i_0_1897,plain,
    ! [X4797,X4798,X4799] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4797),X4798)),X4799))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4797),X4799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_256_add__leD1])]) ).

fof(i_0_1898,plain,
    ! [X4794,X4795,X4796] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4794),X4795)),X4796))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4795),X4796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_255_add__leD2])]) ).

fof(i_0_1899,plain,
    ! [X4755,X4756,X4757] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4755),X4756)),X4757))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4755),X4757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_add__lessD1])]) ).

fof(i_0_1900,plain,
    ! [X4518,X4519,X4520,X4521] :
      ( ~ ordere779506340up_add(X4518)
      | ~ hBOOL(hAPP(X4518,bool,hAPP(X4518,fun(X4518,bool),ord_less_eq(X4518),X4520),X4521))
      | hBOOL(hAPP(X4518,bool,hAPP(X4518,fun(X4518,bool),ord_less_eq(X4518),hAPP(X4518,X4518,hAPP(X4518,fun(X4518,X4518),plus_plus(X4518),X4520),X4519)),hAPP(X4518,X4518,hAPP(X4518,fun(X4518,X4518),plus_plus(X4518),X4521),X4519))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_add__right__mono])])]) ).

fof(i_0_1901,plain,
    ! [X4514,X4515,X4516,X4517] :
      ( ~ ordere779506340up_add(X4514)
      | ~ hBOOL(hAPP(X4514,bool,hAPP(X4514,fun(X4514,bool),ord_less_eq(X4514),X4516),X4517))
      | hBOOL(hAPP(X4514,bool,hAPP(X4514,fun(X4514,bool),ord_less_eq(X4514),hAPP(X4514,X4514,hAPP(X4514,fun(X4514,X4514),plus_plus(X4514),X4515),X4516)),hAPP(X4514,X4514,hAPP(X4514,fun(X4514,X4514),plus_plus(X4514),X4515),X4517))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_add__left__mono])])]) ).

fof(i_0_1902,plain,
    ! [X4547,X4548,X4549,X4550] :
      ( ~ ordere223160158up_add(X4547)
      | ~ hBOOL(hAPP(X4547,bool,hAPP(X4547,fun(X4547,bool),ord_less(X4547),X4549),X4550))
      | hBOOL(hAPP(X4547,bool,hAPP(X4547,fun(X4547,bool),ord_less(X4547),hAPP(X4547,X4547,hAPP(X4547,fun(X4547,X4547),plus_plus(X4547),X4549),X4548)),hAPP(X4547,X4547,hAPP(X4547,fun(X4547,X4547),plus_plus(X4547),X4550),X4548))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_add__strict__right__mono])])]) ).

fof(i_0_1903,plain,
    ! [X4543,X4544,X4545,X4546] :
      ( ~ ordere223160158up_add(X4543)
      | ~ hBOOL(hAPP(X4543,bool,hAPP(X4543,fun(X4543,bool),ord_less(X4543),X4545),X4546))
      | hBOOL(hAPP(X4543,bool,hAPP(X4543,fun(X4543,bool),ord_less(X4543),hAPP(X4543,X4543,hAPP(X4543,fun(X4543,X4543),plus_plus(X4543),X4544),X4545)),hAPP(X4543,X4543,hAPP(X4543,fun(X4543,X4543),plus_plus(X4543),X4544),X4546))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_add__strict__left__mono])])]) ).

fof(i_0_1904,plain,
    ! [X5795,X5796,X5797,X5798,X5799] :
      ( ( hBOOL(hAPP(fun(X5796,bool),bool,hAPP(X5796,fun(fun(X5796,bool),bool),member(X5796),esk134_5(X5795,X5796,X5797,X5798,X5799)),X5799))
        | hAPP(fun(X5796,bool),fun(X5796,X5795),hAPP(fun(X5796,X5795),fun(fun(X5796,bool),fun(X5796,X5795)),restrict(X5796,X5795),X5797),X5799) = hAPP(fun(X5796,bool),fun(X5796,X5795),hAPP(fun(X5796,X5795),fun(fun(X5796,bool),fun(X5796,X5795)),restrict(X5796,X5795),X5798),X5799) )
      & ( hAPP(X5796,X5795,X5797,esk134_5(X5795,X5796,X5797,X5798,X5799)) != hAPP(X5796,X5795,X5798,esk134_5(X5795,X5796,X5797,X5798,X5799))
        | hAPP(fun(X5796,bool),fun(X5796,X5795),hAPP(fun(X5796,X5795),fun(fun(X5796,bool),fun(X5796,X5795)),restrict(X5796,X5795),X5797),X5799) = hAPP(fun(X5796,bool),fun(X5796,X5795),hAPP(fun(X5796,X5795),fun(fun(X5796,bool),fun(X5796,X5795)),restrict(X5796,X5795),X5798),X5799) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_561_restrict__ext])])])]) ).

fof(i_0_1905,plain,
    ! [X7407,X7408,X7409] :
      ( ( hBOOL(hAPP(fun(X7407,bool),bool,hAPP(X7407,fun(fun(X7407,bool),bool),member(X7407),esk172_3(X7407,X7408,X7409)),hAPP(fun(X7407,bool),fun(X7407,bool),hAPP(fun(X7407,bool),fun(fun(X7407,bool),fun(X7407,bool)),semilattice_inf_inf(fun(X7407,bool)),X7409),X7408)))
        | hAPP(fun(X7407,bool),nat,finite_card(X7407),hAPP(fun(X7407,bool),fun(X7407,bool),hAPP(fun(X7407,bool),fun(fun(X7407,bool),fun(X7407,bool)),semilattice_sup_sup(fun(X7407,bool)),X7409),X7408)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7407,bool),nat,finite_card(X7407),X7409)),hAPP(fun(X7407,bool),nat,finite_card(X7407),X7408))
        | ~ hBOOL(hAPP(fun(X7407,bool),bool,finite_finite_1(X7407),X7408))
        | ~ hBOOL(hAPP(fun(X7407,bool),bool,finite_finite_1(X7407),X7409)) )
      & ( one_one(nat) != zero_zero(nat)
        | hAPP(fun(X7407,bool),nat,finite_card(X7407),hAPP(fun(X7407,bool),fun(X7407,bool),hAPP(fun(X7407,bool),fun(fun(X7407,bool),fun(X7407,bool)),semilattice_sup_sup(fun(X7407,bool)),X7409),X7408)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X7407,bool),nat,finite_card(X7407),X7409)),hAPP(fun(X7407,bool),nat,finite_card(X7407),X7408))
        | ~ hBOOL(hAPP(fun(X7407,bool),bool,finite_finite_1(X7407),X7408))
        | ~ hBOOL(hAPP(fun(X7407,bool),bool,finite_finite_1(X7407),X7409)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_967_card_Ounion__inter__neutral])])])]) ).

fof(i_0_1906,plain,
    ! [X7550,X7551,X7552,X7553,X7554] :
      ( ~ comm_monoid_add(X7551)
      | ~ hBOOL(hAPP(fun(X7550,bool),bool,finite_finite_1(X7550),X7554))
      | ~ hBOOL(hAPP(fun(X7550,bool),bool,hAPP(fun(X7550,X7550),fun(fun(X7550,bool),bool),inj_on(X7550,X7550),X7553),X7554))
      | hAPP(fun(X7550,bool),X7551,hAPP(fun(X7550,X7551),fun(fun(X7550,bool),X7551),big_co1399186613setsum(X7550,X7551),X7552),hAPP(fun(X7550,bool),fun(X7550,bool),hAPP(fun(X7550,X7550),fun(fun(X7550,bool),fun(X7550,bool)),image(X7550,X7550),X7553),X7554)) = hAPP(fun(X7550,bool),X7551,hAPP(fun(X7550,X7551),fun(fun(X7550,bool),X7551),big_co1399186613setsum(X7550,X7551),hAPP(fun(X7550,X7550),fun(X7550,X7551),hAPP(fun(X7550,X7551),fun(fun(X7550,X7550),fun(X7550,X7551)),comp(X7550,X7551,X7550),X7552),X7553)),X7554) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_996_setsum_Oreindex])])]) ).

fof(i_0_1907,plain,
    ! [X7473,X7474,X7475,X7476,X7477] :
      ( ~ semiring_0(X7474)
      | hAPP(X7474,X7474,hAPP(X7474,fun(X7474,X7474),times_times(X7474),X7475),hAPP(fun(X7473,bool),X7474,hAPP(fun(X7473,X7474),fun(fun(X7473,bool),X7474),big_co1399186613setsum(X7473,X7474),X7476),X7477)) = hAPP(fun(X7473,bool),X7474,hAPP(fun(X7473,X7474),fun(fun(X7473,bool),X7474),big_co1399186613setsum(X7473,X7474),hAPP(fun(X7473,X7474),fun(X7473,X7474),hAPP(fun(X7474,X7474),fun(fun(X7473,X7474),fun(X7473,X7474)),combb(X7474,X7474,X7473),hAPP(X7474,fun(X7474,X7474),times_times(X7474),X7475)),X7476)),X7477) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_981_setsum__right__distrib])])]) ).

fof(i_0_1908,plain,
    ! [X6284,X6285,X6286,X6287] :
      ( ( hBOOL(hAPP(fun(X6284,bool),bool,hAPP(X6284,fun(fun(X6284,bool),bool),member(X6284),esk136_4(X6284,X6285,X6286,X6287)),X6287))
        | hAPP(fun(X6284,bool),X6285,hAPP(X6285,fun(fun(X6284,bool),X6285),hAPP(fun(X6284,X6285),fun(X6285,fun(fun(X6284,bool),X6285)),hAPP(fun(X6285,fun(X6285,X6285)),fun(fun(X6284,X6285),fun(X6285,fun(fun(X6284,bool),X6285))),finite_fold_image(X6285,X6284),times_times(X6285)),X6286),one_one(X6285)),X6287) = one_one(X6285)
        | ~ hBOOL(hAPP(fun(X6284,bool),bool,finite_finite_1(X6284),X6287))
        | ~ comm_monoid_mult(X6285) )
      & ( hAPP(X6284,X6285,X6286,esk136_4(X6284,X6285,X6286,X6287)) != one_one(X6285)
        | hAPP(fun(X6284,bool),X6285,hAPP(X6285,fun(fun(X6284,bool),X6285),hAPP(fun(X6284,X6285),fun(X6285,fun(fun(X6284,bool),X6285)),hAPP(fun(X6285,fun(X6285,X6285)),fun(fun(X6284,X6285),fun(X6285,fun(fun(X6284,bool),X6285))),finite_fold_image(X6285,X6284),times_times(X6285)),X6286),one_one(X6285)),X6287) = one_one(X6285)
        | ~ hBOOL(hAPP(fun(X6284,bool),bool,finite_finite_1(X6284),X6287))
        | ~ comm_monoid_mult(X6285) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_700_fold__image__1])])])])]) ).

cnf(i_0_1909,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk105_5(X3,X1,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),top_top(fun(X3,bool)))))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1234]) ).

fof(i_0_1910,plain,
    ! [X7235,X7236,X7237,X7238] :
      ( ~ comm_monoid_add(X7235)
      | hAPP(fun(nat,bool),X7235,hAPP(fun(nat,X7235),fun(fun(nat,bool),X7235),big_co1399186613setsum(nat,X7235),X7236),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X7237)),hAPP(nat,nat,suc,X7238))) = hAPP(fun(nat,bool),X7235,hAPP(fun(nat,X7235),fun(fun(nat,bool),X7235),big_co1399186613setsum(nat,X7235),hAPP(fun(nat,nat),fun(nat,X7235),hAPP(fun(nat,X7235),fun(fun(nat,nat),fun(nat,X7235)),combb(nat,X7235,nat),X7236),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X7237),X7238)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_919_setsum__shift__bounds__Suc__ivl])])]) ).

fof(i_0_1911,plain,
    ! [X7118,X7119,X7120,X7121] :
      ( ~ comm_monoid_add(X7118)
      | hAPP(fun(nat,bool),X7118,hAPP(fun(nat,X7118),fun(fun(nat,bool),X7118),big_co1399186613setsum(nat,X7118),X7119),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X7120)),hAPP(nat,nat,suc,X7121))) = hAPP(fun(nat,bool),X7118,hAPP(fun(nat,X7118),fun(fun(nat,bool),X7118),big_co1399186613setsum(nat,X7118),hAPP(fun(nat,nat),fun(nat,X7118),hAPP(fun(nat,X7118),fun(fun(nat,nat),fun(nat,X7118)),combb(nat,X7118,nat),X7119),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7120),X7121)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_889_setsum__shift__bounds__cl__Suc__ivl])])]) ).

fof(i_0_1912,plain,
    ! [X7199,X7200,X7201,X7202] :
      ( ~ hBOOL(hAPP(fun(X7199,bool),bool,hAPP(fun(X7199,bool),fun(fun(X7199,bool),bool),ord_less_eq(fun(X7199,bool)),X7201),X7202))
      | ~ hBOOL(hAPP(fun(X7199,bool),bool,hAPP(fun(X7199,bool),fun(fun(X7199,bool),bool),ord_less_eq(fun(X7199,bool)),X7201),X7200))
      | hBOOL(hAPP(fun(X7199,bool),bool,hAPP(fun(X7199,bool),fun(fun(X7199,bool),bool),ord_less_eq(fun(X7199,bool)),X7201),hAPP(fun(X7199,bool),fun(X7199,bool),hAPP(fun(X7199,bool),fun(fun(X7199,bool),fun(X7199,bool)),semilattice_inf_inf(fun(X7199,bool)),X7202),X7200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_910_Int__greatest])]) ).

fof(i_0_1913,plain,
    ! [X5867,X5868,X5869] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5868),X5869))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5868),X5867)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5869),X5867))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_574_mult__le__mono1])]) ).

fof(i_0_1914,plain,
    ! [X5870,X5871,X5872] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5871),X5872))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5870),X5871)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5870),X5872))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_575_mult__le__mono2])]) ).

fof(i_0_1915,plain,
    ! [X4787,X4788,X4789] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4788),X4789))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4788),X4787)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4789),X4787))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_add__le__mono1])]) ).

fof(i_0_1916,plain,
    ! [X4744,X4745,X4746] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4745),X4746))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4745),X4744)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4746),X4744))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_add__less__mono1])]) ).

fof(i_0_1917,plain,
    ! [X6171,X6172,X6173,X6174] : hBOOL(hAPP(fun(fun(X6171,X6172),bool),bool,hAPP(fun(X6171,X6172),fun(fun(fun(X6171,X6172),bool),bool),member(fun(X6171,X6172)),hAPP(fun(X6171,bool),fun(X6171,X6172),hAPP(fun(X6171,X6172),fun(fun(X6171,bool),fun(X6171,X6172)),restrict(X6171,X6172),X6173),X6174)),hAPP(fun(X6171,bool),fun(fun(X6171,X6172),bool),extensional(X6171,X6172),X6174))),
    inference(variable_rename,[status(thm)],[fact_670_restrict__extensional]) ).

fof(i_0_1918,plain,
    ! [X5507,X5508,X5509] :
      ( ~ hBOOL(hAPP(fun(X5507,bool),bool,finite_finite_1(X5507),X5509))
      | ~ hBOOL(hAPP(fun(X5507,bool),bool,hAPP(fun(X5507,bool),fun(fun(X5507,bool),bool),ord_less_eq(fun(X5507,bool)),X5509),hAPP(fun(X5507,bool),fun(X5507,bool),hAPP(fun(X5507,X5507),fun(fun(X5507,bool),fun(X5507,bool)),image(X5507,X5507),X5508),X5509)))
      | hBOOL(hAPP(fun(X5507,bool),bool,hAPP(fun(X5507,X5507),fun(fun(X5507,bool),bool),inj_on(X5507,X5507),X5508),X5509)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_493_finite__surj__inj])]) ).

fof(i_0_1919,plain,
    ! [X5608,X5609,X5610] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),X5608)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X5609),X5610)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5609),X5608)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5610),X5608)),
    inference(variable_rename,[status(thm)],[fact_517_image__add__atLeastLessThan]) ).

fof(i_0_1920,plain,
    ! [X6646,X6647,X6648] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),X6646)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X6647),X6648)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6647),X6646)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6648),X6646)),
    inference(variable_rename,[status(thm)],[fact_768_image__add__atLeastAtMost]) ).

fof(i_0_1921,plain,
    ! [X6061,X6062,X6063] :
      ( ( ~ hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),zero_zero(X6061)),X6063))
        | ~ hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),X6062),zero_zero(X6061)))
        | hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),hAPP(X6061,X6061,hAPP(X6061,fun(X6061,X6061),times_times(X6061),X6063),X6062)),zero_zero(X6061)))
        | ~ ordere453448008miring(X6061) )
      & ( ~ hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),X6063),zero_zero(X6061)))
        | ~ hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),zero_zero(X6061)),X6062))
        | hBOOL(hAPP(X6061,bool,hAPP(X6061,fun(X6061,bool),ord_less_eq(X6061),hAPP(X6061,X6061,hAPP(X6061,fun(X6061,X6061),times_times(X6061),X6063),X6062)),zero_zero(X6061)))
        | ~ ordere453448008miring(X6061) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_635_split__mult__neg__le])])])]) ).

fof(i_0_1922,plain,
    ! [X6022,X6023,X6024] :
      ( ~ ordere453448008miring(X6022)
      | ~ hBOOL(hAPP(X6022,bool,hAPP(X6022,fun(X6022,bool),ord_less_eq(X6022),X6024),zero_zero(X6022)))
      | ~ hBOOL(hAPP(X6022,bool,hAPP(X6022,fun(X6022,bool),ord_less_eq(X6022),zero_zero(X6022)),X6023))
      | hBOOL(hAPP(X6022,bool,hAPP(X6022,fun(X6022,bool),ord_less_eq(X6022),hAPP(X6022,X6022,hAPP(X6022,fun(X6022,X6022),times_times(X6022),X6024),X6023)),zero_zero(X6022))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_625_mult__nonpos__nonneg])])]) ).

fof(i_0_1923,plain,
    ! [X6016,X6017,X6018] :
      ( ~ ordere453448008miring(X6016)
      | ~ hBOOL(hAPP(X6016,bool,hAPP(X6016,fun(X6016,bool),ord_less_eq(X6016),zero_zero(X6016)),X6018))
      | ~ hBOOL(hAPP(X6016,bool,hAPP(X6016,fun(X6016,bool),ord_less_eq(X6016),X6017),zero_zero(X6016)))
      | hBOOL(hAPP(X6016,bool,hAPP(X6016,fun(X6016,bool),ord_less_eq(X6016),hAPP(X6016,X6016,hAPP(X6016,fun(X6016,X6016),times_times(X6016),X6018),X6017)),zero_zero(X6016))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_623_mult__nonneg__nonpos])])]) ).

fof(i_0_1924,plain,
    ! [X6019,X6020,X6021] :
      ( ~ ordere453448008miring(X6019)
      | ~ hBOOL(hAPP(X6019,bool,hAPP(X6019,fun(X6019,bool),ord_less_eq(X6019),zero_zero(X6019)),X6021))
      | ~ hBOOL(hAPP(X6019,bool,hAPP(X6019,fun(X6019,bool),ord_less_eq(X6019),X6020),zero_zero(X6019)))
      | hBOOL(hAPP(X6019,bool,hAPP(X6019,fun(X6019,bool),ord_less_eq(X6019),hAPP(X6019,X6019,hAPP(X6019,fun(X6019,X6019),times_times(X6019),X6020),X6021)),zero_zero(X6019))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_624_mult__nonneg__nonpos2])])]) ).

fof(i_0_1925,plain,
    ! [X6097,X6098,X6099] :
      ( ~ linord20386208strict(X6097)
      | ~ hBOOL(hAPP(X6097,bool,hAPP(X6097,fun(X6097,bool),ord_less(X6097),X6099),zero_zero(X6097)))
      | ~ hBOOL(hAPP(X6097,bool,hAPP(X6097,fun(X6097,bool),ord_less(X6097),zero_zero(X6097)),X6098))
      | hBOOL(hAPP(X6097,bool,hAPP(X6097,fun(X6097,bool),ord_less(X6097),hAPP(X6097,X6097,hAPP(X6097,fun(X6097,X6097),times_times(X6097),X6099),X6098)),zero_zero(X6097))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_646_mult__neg__pos])])]) ).

fof(i_0_1926,plain,
    ! [X6081,X6082,X6083] :
      ( ~ linord20386208strict(X6081)
      | ~ hBOOL(hAPP(X6081,bool,hAPP(X6081,fun(X6081,bool),ord_less(X6081),zero_zero(X6081)),X6083))
      | ~ hBOOL(hAPP(X6081,bool,hAPP(X6081,fun(X6081,bool),ord_less(X6081),X6082),zero_zero(X6081)))
      | hBOOL(hAPP(X6081,bool,hAPP(X6081,fun(X6081,bool),ord_less(X6081),hAPP(X6081,X6081,hAPP(X6081,fun(X6081,X6081),times_times(X6081),X6083),X6082)),zero_zero(X6081))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_641_mult__pos__neg])])]) ).

fof(i_0_1927,plain,
    ! [X6084,X6085,X6086] :
      ( ~ linord20386208strict(X6084)
      | ~ hBOOL(hAPP(X6084,bool,hAPP(X6084,fun(X6084,bool),ord_less(X6084),zero_zero(X6084)),X6086))
      | ~ hBOOL(hAPP(X6084,bool,hAPP(X6084,fun(X6084,bool),ord_less(X6084),X6085),zero_zero(X6084)))
      | hBOOL(hAPP(X6084,bool,hAPP(X6084,fun(X6084,bool),ord_less(X6084),hAPP(X6084,X6084,hAPP(X6084,fun(X6084,X6084),times_times(X6084),X6085),X6086)),zero_zero(X6084))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_642_mult__pos__neg2])])]) ).

fof(i_0_1928,plain,
    ! [X5049,X5050,X5051] :
      ( ~ ordere216010020id_add(X5049)
      | ~ hBOOL(hAPP(X5049,bool,hAPP(X5049,fun(X5049,bool),ord_less_eq(X5049),X5051),zero_zero(X5049)))
      | ~ hBOOL(hAPP(X5049,bool,hAPP(X5049,fun(X5049,bool),ord_less_eq(X5049),X5050),zero_zero(X5049)))
      | hBOOL(hAPP(X5049,bool,hAPP(X5049,fun(X5049,bool),ord_less_eq(X5049),hAPP(X5049,X5049,hAPP(X5049,fun(X5049,X5049),plus_plus(X5049),X5051),X5050)),zero_zero(X5049))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_add__nonpos__nonpos])])]) ).

fof(i_0_1929,plain,
    ! [X5095,X5096,X5097] :
      ( ~ ordere216010020id_add(X5095)
      | ~ hBOOL(hAPP(X5095,bool,hAPP(X5095,fun(X5095,bool),ord_less(X5095),X5097),zero_zero(X5095)))
      | ~ hBOOL(hAPP(X5095,bool,hAPP(X5095,fun(X5095,bool),ord_less_eq(X5095),X5096),zero_zero(X5095)))
      | hBOOL(hAPP(X5095,bool,hAPP(X5095,fun(X5095,bool),ord_less(X5095),hAPP(X5095,X5095,hAPP(X5095,fun(X5095,X5095),plus_plus(X5095),X5097),X5096)),zero_zero(X5095))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_add__neg__nonpos])])]) ).

fof(i_0_1930,plain,
    ! [X5092,X5093,X5094] :
      ( ~ ordere216010020id_add(X5092)
      | ~ hBOOL(hAPP(X5092,bool,hAPP(X5092,fun(X5092,bool),ord_less_eq(X5092),X5094),zero_zero(X5092)))
      | ~ hBOOL(hAPP(X5092,bool,hAPP(X5092,fun(X5092,bool),ord_less(X5092),X5093),zero_zero(X5092)))
      | hBOOL(hAPP(X5092,bool,hAPP(X5092,fun(X5092,bool),ord_less(X5092),hAPP(X5092,X5092,hAPP(X5092,fun(X5092,X5092),plus_plus(X5092),X5094),X5093)),zero_zero(X5092))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_add__nonpos__neg])])]) ).

fof(i_0_1931,plain,
    ! [X5070,X5071,X5072] :
      ( ~ ordere216010020id_add(X5070)
      | ~ hBOOL(hAPP(X5070,bool,hAPP(X5070,fun(X5070,bool),ord_less(X5070),X5072),zero_zero(X5070)))
      | ~ hBOOL(hAPP(X5070,bool,hAPP(X5070,fun(X5070,bool),ord_less(X5070),X5071),zero_zero(X5070)))
      | hBOOL(hAPP(X5070,bool,hAPP(X5070,fun(X5070,bool),ord_less(X5070),hAPP(X5070,X5070,hAPP(X5070,fun(X5070,X5070),plus_plus(X5070),X5072),X5071)),zero_zero(X5070))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_add__neg__neg])])]) ).

fof(i_0_1932,plain,
    ! [X6956,X6957,X6958,X6959] :
      ( ~ semilattice_sup(X6956)
      | ~ hBOOL(hAPP(X6956,bool,hAPP(X6956,fun(X6956,bool),ord_less_eq(X6956),X6958),X6959))
      | ~ hBOOL(hAPP(X6956,bool,hAPP(X6956,fun(X6956,bool),ord_less_eq(X6956),X6957),X6959))
      | hBOOL(hAPP(X6956,bool,hAPP(X6956,fun(X6956,bool),ord_less_eq(X6956),hAPP(X6956,X6956,hAPP(X6956,fun(X6956,X6956),semilattice_sup_sup(X6956),X6958),X6957)),X6959)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_847_sup__least])])]) ).

fof(i_0_1933,plain,
    ! [X6952,X6953,X6954,X6955] :
      ( ~ semilattice_sup(X6952)
      | ~ hBOOL(hAPP(X6952,bool,hAPP(X6952,fun(X6952,bool),ord_less_eq(X6952),X6954),X6955))
      | ~ hBOOL(hAPP(X6952,bool,hAPP(X6952,fun(X6952,bool),ord_less_eq(X6952),X6953),X6955))
      | hBOOL(hAPP(X6952,bool,hAPP(X6952,fun(X6952,bool),ord_less_eq(X6952),hAPP(X6952,X6952,hAPP(X6952,fun(X6952,X6952),semilattice_sup_sup(X6952),X6954),X6953)),X6955)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_846_le__supI])])]) ).

fof(i_0_1934,plain,
    ! [X7215,X7216,X7217,X7218,X7219] :
      ( ~ hBOOL(hAPP(fun(X7215,bool),bool,hAPP(fun(X7215,X7216),fun(fun(X7215,bool),bool),inj_on(X7215,X7216),X7218),X7219))
      | ~ hBOOL(hAPP(fun(X7215,bool),bool,hAPP(fun(X7215,X7216),fun(fun(X7215,bool),bool),inj_on(X7215,X7216),X7218),X7217))
      | hBOOL(hAPP(fun(X7215,bool),bool,hAPP(fun(X7215,X7216),fun(fun(X7215,bool),bool),inj_on(X7215,X7216),X7218),hAPP(fun(X7215,bool),fun(X7215,bool),hAPP(fun(X7215,bool),fun(fun(X7215,bool),fun(X7215,bool)),semilattice_inf_inf(fun(X7215,bool)),X7219),X7217))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_915_inj__on__Int])]) ).

cnf(i_0_1935,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk109_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_1243]) ).

cnf(i_0_1936,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk103_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_1244]) ).

fof(i_0_1937,plain,
    ! [X7520,X7521,X7522,X7523,X7524,X7525] :
      ( ~ comm_monoid_add(X7522)
      | ~ hBOOL(hAPP(fun(X7520,bool),bool,hAPP(fun(X7520,X7521),fun(fun(X7520,bool),bool),inj_on(X7520,X7521),X7524),X7525))
      | hAPP(fun(X7521,bool),X7522,hAPP(fun(X7521,X7522),fun(fun(X7521,bool),X7522),big_co1399186613setsum(X7521,X7522),X7523),hAPP(fun(X7520,bool),fun(X7521,bool),hAPP(fun(X7520,X7521),fun(fun(X7520,bool),fun(X7521,bool)),image(X7520,X7521),X7524),X7525)) = hAPP(fun(X7520,bool),X7522,hAPP(fun(X7520,X7522),fun(fun(X7520,bool),X7522),big_co1399186613setsum(X7520,X7522),hAPP(fun(X7520,X7521),fun(X7520,X7522),hAPP(fun(X7521,X7522),fun(fun(X7520,X7521),fun(X7520,X7522)),comp(X7521,X7522,X7520),X7523),X7524)),X7525) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_991_setsum__reindex])])]) ).

fof(i_0_1938,plain,
    ! [X6064,X6065] :
      ( ~ linordered_ring(X6064)
      | ~ hBOOL(hAPP(X6064,bool,hAPP(X6064,fun(X6064,bool),ord_less(X6064),hAPP(X6064,X6064,hAPP(X6064,fun(X6064,X6064),times_times(X6064),X6065),X6065)),zero_zero(X6064))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1245])])]) ).

fof(i_0_1939,plain,
    ! [X6842,X6843,X6844,X6845] :
      ( ~ linorder(X6842)
      | ~ hBOOL(hAPP(X6842,bool,hAPP(X6842,fun(X6842,bool),ord_less(X6842),X6844),X6845))
      | ~ hBOOL(hAPP(X6842,bool,hAPP(X6842,fun(X6842,bool),ord_less_eq(X6842),X6845),X6843))
      | hAPP(fun(X6842,bool),fun(X6842,bool),hAPP(fun(X6842,bool),fun(fun(X6842,bool),fun(X6842,bool)),semilattice_sup_sup(fun(X6842,bool)),hAPP(X6842,fun(X6842,bool),hAPP(X6842,fun(X6842,fun(X6842,bool)),ord_gr676655987ssThan(X6842),X6844),X6845)),hAPP(X6842,fun(X6842,bool),hAPP(X6842,fun(X6842,fun(X6842,bool)),ord_atLeastLessThan(X6842),X6845),X6843)) = hAPP(X6842,fun(X6842,bool),hAPP(X6842,fun(X6842,fun(X6842,bool)),ord_gr676655987ssThan(X6842),X6844),X6843) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_814_ivl__disj__un_I15_J])])]) ).

fof(i_0_1940,plain,
    ! [X6664,X6665,X6666,X6667] :
      ( ~ linorder(X6664)
      | ~ hBOOL(hAPP(X6664,bool,hAPP(X6664,fun(X6664,bool),ord_less(X6664),X6666),X6667))
      | ~ hBOOL(hAPP(X6664,bool,hAPP(X6664,fun(X6664,bool),ord_less_eq(X6664),X6667),X6665))
      | hAPP(fun(X6664,bool),fun(X6664,bool),hAPP(fun(X6664,bool),fun(fun(X6664,bool),fun(X6664,bool)),semilattice_sup_sup(fun(X6664,bool)),hAPP(X6664,fun(X6664,bool),hAPP(X6664,fun(X6664,fun(X6664,bool)),ord_gr676655987ssThan(X6664),X6666),X6667)),hAPP(X6664,fun(X6664,bool),hAPP(X6664,fun(X6664,fun(X6664,bool)),ord_atLeastAtMost(X6664),X6667),X6665)) = hAPP(X6664,fun(X6664,bool),hAPP(X6664,fun(X6664,fun(X6664,bool)),ord_gr1471790799AtMost(X6664),X6666),X6665) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_772_ivl__disj__un_I19_J])])]) ).

fof(i_0_1941,plain,
    ! [X6846,X6847,X6848,X6849] :
      ( ~ linorder(X6846)
      | ~ hBOOL(hAPP(X6846,bool,hAPP(X6846,fun(X6846,bool),ord_less_eq(X6846),X6848),X6849))
      | ~ hBOOL(hAPP(X6846,bool,hAPP(X6846,fun(X6846,bool),ord_less(X6846),X6849),X6847))
      | hAPP(fun(X6846,bool),fun(X6846,bool),hAPP(fun(X6846,bool),fun(fun(X6846,bool),fun(X6846,bool)),semilattice_sup_sup(fun(X6846,bool)),hAPP(X6846,fun(X6846,bool),hAPP(X6846,fun(X6846,fun(X6846,bool)),ord_gr1471790799AtMost(X6846),X6848),X6849)),hAPP(X6846,fun(X6846,bool),hAPP(X6846,fun(X6846,fun(X6846,bool)),ord_gr676655987ssThan(X6846),X6849),X6847)) = hAPP(X6846,fun(X6846,bool),hAPP(X6846,fun(X6846,fun(X6846,bool)),ord_gr676655987ssThan(X6846),X6848),X6847) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_815_ivl__disj__un_I16_J])])]) ).

fof(i_0_1942,plain,
    ! [X6688,X6689,X6690,X6691] :
      ( ~ linorder(X6688)
      | ~ hBOOL(hAPP(X6688,bool,hAPP(X6688,fun(X6688,bool),ord_less_eq(X6688),X6690),X6691))
      | ~ hBOOL(hAPP(X6688,bool,hAPP(X6688,fun(X6688,bool),ord_less_eq(X6688),X6691),X6689))
      | hAPP(fun(X6688,bool),fun(X6688,bool),hAPP(fun(X6688,bool),fun(fun(X6688,bool),fun(X6688,bool)),semilattice_sup_sup(fun(X6688,bool)),hAPP(X6688,fun(X6688,bool),hAPP(X6688,fun(X6688,fun(X6688,bool)),ord_gr1471790799AtMost(X6688),X6690),X6691)),hAPP(X6688,fun(X6688,bool),hAPP(X6688,fun(X6688,fun(X6688,bool)),ord_gr1471790799AtMost(X6688),X6691),X6689)) = hAPP(X6688,fun(X6688,bool),hAPP(X6688,fun(X6688,fun(X6688,bool)),ord_gr1471790799AtMost(X6688),X6690),X6689) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_778_ivl__disj__un_I20_J])])]) ).

fof(i_0_1943,plain,
    ! [X6692,X6693,X6694,X6695] :
      ( ~ linorder(X6692)
      | ~ hBOOL(hAPP(X6692,bool,hAPP(X6692,fun(X6692,bool),ord_less_eq(X6692),X6694),X6695))
      | ~ hBOOL(hAPP(X6692,bool,hAPP(X6692,fun(X6692,bool),ord_less_eq(X6692),X6695),X6693))
      | hAPP(fun(X6692,bool),fun(X6692,bool),hAPP(fun(X6692,bool),fun(fun(X6692,bool),fun(X6692,bool)),semilattice_sup_sup(fun(X6692,bool)),hAPP(X6692,fun(X6692,bool),hAPP(X6692,fun(X6692,fun(X6692,bool)),ord_atLeastLessThan(X6692),X6694),X6695)),hAPP(X6692,fun(X6692,bool),hAPP(X6692,fun(X6692,fun(X6692,bool)),ord_atLeastLessThan(X6692),X6695),X6693)) = hAPP(X6692,fun(X6692,bool),hAPP(X6692,fun(X6692,fun(X6692,bool)),ord_atLeastLessThan(X6692),X6694),X6693) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_779_ivl__disj__un_I17_J])])]) ).

fof(i_0_1944,plain,
    ! [X6822,X6823,X6824,X6825] :
      ( ~ linorder(X6822)
      | ~ hBOOL(hAPP(X6822,bool,hAPP(X6822,fun(X6822,bool),ord_less_eq(X6822),X6824),X6825))
      | ~ hBOOL(hAPP(X6822,bool,hAPP(X6822,fun(X6822,bool),ord_less_eq(X6822),X6825),X6823))
      | hAPP(fun(X6822,bool),fun(X6822,bool),hAPP(fun(X6822,bool),fun(fun(X6822,bool),fun(X6822,bool)),semilattice_sup_sup(fun(X6822,bool)),hAPP(X6822,fun(X6822,bool),hAPP(X6822,fun(X6822,fun(X6822,bool)),ord_atLeastLessThan(X6822),X6824),X6825)),hAPP(X6822,fun(X6822,bool),hAPP(X6822,fun(X6822,fun(X6822,bool)),ord_atLeastAtMost(X6822),X6825),X6823)) = hAPP(X6822,fun(X6822,bool),hAPP(X6822,fun(X6822,fun(X6822,bool)),ord_atLeastAtMost(X6822),X6824),X6823) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_809_ivl__disj__un_I21_J])])]) ).

fof(i_0_1945,plain,
    ! [X6668,X6669,X6670,X6671] :
      ( ~ linorder(X6668)
      | ~ hBOOL(hAPP(X6668,bool,hAPP(X6668,fun(X6668,bool),ord_less_eq(X6668),X6670),X6671))
      | ~ hBOOL(hAPP(X6668,bool,hAPP(X6668,fun(X6668,bool),ord_less(X6668),X6671),X6669))
      | hAPP(fun(X6668,bool),fun(X6668,bool),hAPP(fun(X6668,bool),fun(fun(X6668,bool),fun(X6668,bool)),semilattice_sup_sup(fun(X6668,bool)),hAPP(X6668,fun(X6668,bool),hAPP(X6668,fun(X6668,fun(X6668,bool)),ord_atLeastAtMost(X6668),X6670),X6671)),hAPP(X6668,fun(X6668,bool),hAPP(X6668,fun(X6668,fun(X6668,bool)),ord_gr676655987ssThan(X6668),X6671),X6669)) = hAPP(X6668,fun(X6668,bool),hAPP(X6668,fun(X6668,fun(X6668,bool)),ord_atLeastLessThan(X6668),X6670),X6669) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_773_ivl__disj__un_I18_J])])]) ).

fof(i_0_1946,plain,
    ! [X6829,X6830,X6831,X6832] :
      ( ~ linorder(X6829)
      | ~ hBOOL(hAPP(X6829,bool,hAPP(X6829,fun(X6829,bool),ord_less_eq(X6829),X6831),X6832))
      | ~ hBOOL(hAPP(X6829,bool,hAPP(X6829,fun(X6829,bool),ord_less_eq(X6829),X6832),X6830))
      | hAPP(fun(X6829,bool),fun(X6829,bool),hAPP(fun(X6829,bool),fun(fun(X6829,bool),fun(X6829,bool)),semilattice_sup_sup(fun(X6829,bool)),hAPP(X6829,fun(X6829,bool),hAPP(X6829,fun(X6829,fun(X6829,bool)),ord_atLeastAtMost(X6829),X6831),X6832)),hAPP(X6829,fun(X6829,bool),hAPP(X6829,fun(X6829,fun(X6829,bool)),ord_gr1471790799AtMost(X6829),X6832),X6830)) = hAPP(X6829,fun(X6829,bool),hAPP(X6829,fun(X6829,fun(X6829,bool)),ord_atLeastAtMost(X6829),X6831),X6830) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_811_ivl__disj__un_I22_J])])]) ).

fof(i_0_1947,plain,
    ! [X6538,X6539,X6540,X6541,X6542,X6543] :
      ( ~ hBOOL(hAPP(fun(fun(X6538,bool),fun(X6539,X6539)),bool,hAPP(fun(X6538,fun(X6539,X6539)),fun(fun(fun(X6538,bool),fun(X6539,X6539)),bool),finite_folding_idem(X6538,X6539),X6542),X6543))
      | ~ hBOOL(hAPP(fun(X6538,bool),bool,finite_finite_1(X6538),X6541))
      | ~ hBOOL(hAPP(fun(X6538,bool),bool,hAPP(fun(X6538,bool),fun(fun(X6538,bool),bool),ord_less_eq(fun(X6538,bool)),X6540),X6541))
      | hAPP(fun(X6539,X6539),fun(X6539,X6539),hAPP(fun(X6539,X6539),fun(fun(X6539,X6539),fun(X6539,X6539)),comp(X6539,X6539,X6539),hAPP(fun(X6538,bool),fun(X6539,X6539),X6543,X6541)),hAPP(fun(X6538,bool),fun(X6539,X6539),X6543,X6540)) = hAPP(fun(X6538,bool),fun(X6539,X6539),X6543,X6541) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_747_folding__idem_Osubset__comp__idem])]) ).

fof(i_0_1948,plain,
    ! [X6836,X6837,X6838,X6839,X6840,X6841] :
      ( ~ hBOOL(hAPP(fun(fun(X6836,bool),fun(X6837,X6837)),bool,hAPP(fun(X6836,fun(X6837,X6837)),fun(fun(fun(X6836,bool),fun(X6837,X6837)),bool),finite_folding_idem(X6836,X6837),X6840),X6841))
      | ~ hBOOL(hAPP(fun(X6836,bool),bool,finite_finite_1(X6836),X6839))
      | ~ hBOOL(hAPP(fun(X6836,bool),bool,finite_finite_1(X6836),X6838))
      | hAPP(fun(X6836,bool),fun(X6837,X6837),X6841,hAPP(fun(X6836,bool),fun(X6836,bool),hAPP(fun(X6836,bool),fun(fun(X6836,bool),fun(X6836,bool)),semilattice_sup_sup(fun(X6836,bool)),X6839),X6838)) = hAPP(fun(X6837,X6837),fun(X6837,X6837),hAPP(fun(X6837,X6837),fun(fun(X6837,X6837),fun(X6837,X6837)),comp(X6837,X6837,X6837),hAPP(fun(X6836,bool),fun(X6837,X6837),X6841,X6839)),hAPP(fun(X6836,bool),fun(X6837,X6837),X6841,X6838)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_813_folding__idem_Ounion__idem])]) ).

fof(i_0_1949,plain,
    ! [X7403,X7404,X7405,X7406] :
      ( ~ comm_monoid_add(X7403)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7405),X7406))
      | hAPP(fun(nat,bool),X7403,hAPP(fun(nat,X7403),fun(fun(nat,bool),X7403),big_co1399186613setsum(nat,X7403),X7404),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X7405),X7406)) = hAPP(X7403,X7403,hAPP(X7403,fun(X7403,X7403),plus_plus(X7403),hAPP(nat,X7403,X7404,X7405)),hAPP(fun(nat,bool),X7403,hAPP(fun(nat,X7403),fun(fun(nat,bool),X7403),big_co1399186613setsum(nat,X7403),X7404),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X7405),X7406))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_966_setsum__head])])]) ).

cnf(i_0_1950,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_1246]) ).

fof(i_0_1951,plain,
    ! [X4376,X4377] : hBOOL(hAPP(fun(fun(X4376,X4376),bool),bool,hAPP(fun(X4376,X4376),fun(fun(fun(X4376,X4376),bool),bool),member(fun(X4376,X4376)),combi(X4376)),hAPP(fun(X4376,fun(X4376,bool)),fun(fun(X4376,X4376),bool),hAPP(fun(X4376,bool),fun(fun(X4376,fun(X4376,bool)),fun(fun(X4376,X4376),bool)),pi(X4376,X4376),X4377),hAPP(fun(X4376,bool),fun(X4376,fun(X4376,bool)),combk(fun(X4376,bool),X4376),X4377)))),
    inference(variable_rename,[status(thm)],[fact_144_funcset__id]) ).

fof(i_0_1952,plain,
    ! [X4731,X4732] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4731),X4732)),X4731)),
    inference(variable_rename,[status(thm)],[i_0_1247]) ).

fof(i_0_1953,plain,
    ! [X4733,X4734] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4733),X4734)),X4734)),
    inference(variable_rename,[status(thm)],[i_0_1248]) ).

fof(i_0_1954,plain,
    ! [X7175,X7176,X7177,X7178] :
      ( ( hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),X7177))
        | ~ hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),hAPP(fun(X7175,bool),fun(X7175,bool),hAPP(fun(X7175,bool),fun(fun(X7175,bool),fun(X7175,bool)),semilattice_inf_inf(fun(X7175,bool)),X7177),X7178))) )
      & ( hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),X7178))
        | ~ hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),hAPP(fun(X7175,bool),fun(X7175,bool),hAPP(fun(X7175,bool),fun(fun(X7175,bool),fun(X7175,bool)),semilattice_inf_inf(fun(X7175,bool)),X7177),X7178))) )
      & ( ~ hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),X7177))
        | ~ hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),X7178))
        | hBOOL(hAPP(fun(X7175,bool),bool,hAPP(X7175,fun(fun(X7175,bool),bool),member(X7175),X7176),hAPP(fun(X7175,bool),fun(X7175,bool),hAPP(fun(X7175,bool),fun(fun(X7175,bool),fun(X7175,bool)),semilattice_inf_inf(fun(X7175,bool)),X7177),X7178))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_903_Int__iff])])]) ).

fof(i_0_1955,plain,
    ! [X7042,X7043,X7044,X7045] :
      ( ~ hBOOL(hAPP(fun(X7042,bool),bool,hAPP(X7042,fun(fun(X7042,bool),bool),member(X7042),X7044),X7045))
      | ~ hBOOL(hAPP(fun(X7042,bool),bool,hAPP(X7042,fun(fun(X7042,bool),bool),member(X7042),X7044),X7043))
      | hBOOL(hAPP(fun(X7042,bool),bool,hAPP(X7042,fun(fun(X7042,bool),bool),member(X7042),X7044),hAPP(fun(X7042,bool),fun(X7042,bool),hAPP(fun(X7042,bool),fun(fun(X7042,bool),fun(X7042,bool)),semilattice_inf_inf(fun(X7042,bool)),X7045),X7043))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_870_IntI])]) ).

cnf(i_0_1956,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_1239]) ).

fof(i_0_1957,plain,
    ! [X6560,X6561,X6562,X6563,X6564,X6565] :
      ( ~ hBOOL(hAPP(fun(fun(X6560,bool),fun(X6561,X6561)),bool,hAPP(fun(X6560,fun(X6561,X6561)),fun(fun(fun(X6560,bool),fun(X6561,X6561)),bool),finite_folding_idem(X6560,X6561),X6564),X6565))
      | ~ hBOOL(hAPP(fun(X6560,bool),bool,finite_finite_1(X6560),X6563))
      | ~ hBOOL(hAPP(fun(X6560,bool),bool,hAPP(X6560,fun(fun(X6560,bool),bool),member(X6560),X6562),X6563))
      | hAPP(fun(X6561,X6561),fun(X6561,X6561),hAPP(fun(X6561,X6561),fun(fun(X6561,X6561),fun(X6561,X6561)),comp(X6561,X6561,X6561),hAPP(fun(X6560,bool),fun(X6561,X6561),X6565,X6563)),hAPP(X6560,fun(X6561,X6561),X6564,X6562)) = hAPP(fun(X6560,bool),fun(X6561,X6561),X6565,X6563) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_751_folding__idem_Oin__comp__idem])]) ).

cnf(i_0_1958,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ti(X1,X2) != ti(X1,X3)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1228]) ).

cnf(i_0_1959,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ti(X1,X2) != ti(X1,X3)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1227]) ).

cnf(i_0_1960,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
    | ti(X1,X2) != ti(X1,X3)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1228]) ).

cnf(i_0_1961,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
    | ti(X1,X2) != ti(X1,X3)
    | ~ semiri456707255roduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1227]) ).

fof(i_0_1962,plain,
    ! [X7167,X7168,X7169,X7170] :
      ( ~ hBOOL(hAPP(fun(X7167,bool),bool,hAPP(X7167,fun(fun(X7167,bool),bool),member(X7167),X7168),hAPP(fun(X7167,bool),fun(X7167,bool),hAPP(fun(X7167,bool),fun(fun(X7167,bool),fun(X7167,bool)),semilattice_inf_inf(fun(X7167,bool)),X7169),X7170)))
      | hBOOL(hAPP(fun(X7167,bool),bool,hAPP(X7167,fun(fun(X7167,bool),bool),member(X7167),X7168),X7169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_901_IntD1])]) ).

fof(i_0_1963,plain,
    ! [X7038,X7039,X7040,X7041] :
      ( ( hBOOL(hAPP(fun(X7038,bool),bool,hAPP(X7038,fun(fun(X7038,bool),bool),member(X7038),X7039),X7040))
        | ~ hBOOL(hAPP(fun(X7038,bool),bool,hAPP(X7038,fun(fun(X7038,bool),bool),member(X7038),X7039),hAPP(fun(X7038,bool),fun(X7038,bool),hAPP(fun(X7038,bool),fun(fun(X7038,bool),fun(X7038,bool)),semilattice_inf_inf(fun(X7038,bool)),X7040),X7041))) )
      & ( hBOOL(hAPP(fun(X7038,bool),bool,hAPP(X7038,fun(fun(X7038,bool),bool),member(X7038),X7039),X7041))
        | ~ hBOOL(hAPP(fun(X7038,bool),bool,hAPP(X7038,fun(fun(X7038,bool),bool),member(X7038),X7039),hAPP(fun(X7038,bool),fun(X7038,bool),hAPP(fun(X7038,bool),fun(fun(X7038,bool),fun(X7038,bool)),semilattice_inf_inf(fun(X7038,bool)),X7040),X7041))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1249])])]) ).

fof(i_0_1964,plain,
    ! [X7163,X7164,X7165,X7166] :
      ( ~ hBOOL(hAPP(fun(X7163,bool),bool,hAPP(X7163,fun(fun(X7163,bool),bool),member(X7163),X7164),hAPP(fun(X7163,bool),fun(X7163,bool),hAPP(fun(X7163,bool),fun(fun(X7163,bool),fun(X7163,bool)),semilattice_inf_inf(fun(X7163,bool)),X7165),X7166)))
      | hBOOL(hAPP(fun(X7163,bool),bool,hAPP(X7163,fun(fun(X7163,bool),bool),member(X7163),X7164),X7166)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_900_IntD2])]) ).

cnf(i_0_1965,plain,
    ( 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)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) = ti(fun(X1,bool),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_1250]) ).

cnf(i_0_1966,plain,
    ( 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)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) = ti(fun(X1,bool),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_1251]) ).

fof(i_0_1967,plain,
    ! [X5324,X5325] :
      ( ~ hBOOL(hAPP(fun(X5324,bool),bool,finite_finite_1(X5324),X5325))
      | hAPP(fun(X5324,bool),nat,finite_card(X5324),X5325) = hAPP(fun(X5324,bool),nat,hAPP(nat,fun(fun(X5324,bool),nat),hAPP(fun(X5324,nat),fun(nat,fun(fun(X5324,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X5324,nat),fun(nat,fun(fun(X5324,bool),nat))),finite_fold_image(nat,X5324),plus_plus(nat)),hAPP(nat,fun(X5324,nat),combk(nat,X5324),one_one(nat))),zero_zero(nat)),X5325) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_456_card_Oeq__fold__g])]) ).

fof(i_0_1968,plain,
    ! [X5322,X5323] :
      ( ( ~ hBOOL(hAPP(fun(X5322,bool),bool,finite_finite_1(X5322),X5323))
        | hAPP(fun(X5322,bool),nat,finite_card(X5322),X5323) = hAPP(fun(X5322,bool),nat,hAPP(nat,fun(fun(X5322,bool),nat),hAPP(fun(X5322,nat),fun(nat,fun(fun(X5322,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X5322,nat),fun(nat,fun(fun(X5322,bool),nat))),finite_fold_image(nat,X5322),plus_plus(nat)),hAPP(nat,fun(X5322,nat),combk(nat,X5322),one_one(nat))),zero_zero(nat)),X5323) )
      & ( hBOOL(hAPP(fun(X5322,bool),bool,finite_finite_1(X5322),X5323))
        | hAPP(fun(X5322,bool),nat,finite_card(X5322),X5323) = zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1252])]) ).

fof(i_0_1969,plain,
    ! [X5432,X5433,X5434,X5435,X5436] :
      ( ~ hBOOL(hAPP(fun(X5433,bool),bool,finite_finite_1(X5433),X5436))
      | ~ hBOOL(hAPP(fun(X5432,bool),bool,hAPP(fun(X5432,bool),fun(fun(X5432,bool),bool),ord_less_eq(fun(X5432,bool)),X5434),hAPP(fun(X5433,bool),fun(X5432,bool),hAPP(fun(X5433,X5432),fun(fun(X5433,bool),fun(X5432,bool)),image(X5433,X5432),X5435),X5436)))
      | hBOOL(hAPP(fun(X5432,bool),bool,finite_finite_1(X5432),X5434)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_478_finite__surj])]) ).

fof(i_0_1970,plain,
    ! [X6090,X6091,X6092] :
      ( ~ linord20386208strict(X6090)
      | ~ hBOOL(hAPP(X6090,bool,hAPP(X6090,fun(X6090,bool),ord_less(X6090),zero_zero(X6090)),hAPP(X6090,X6090,hAPP(X6090,fun(X6090,X6090),times_times(X6090),X6091),X6092)))
      | ~ hBOOL(hAPP(X6090,bool,hAPP(X6090,fun(X6090,bool),ord_less(X6090),zero_zero(X6090)),X6092))
      | hBOOL(hAPP(X6090,bool,hAPP(X6090,fun(X6090,bool),ord_less(X6090),zero_zero(X6090)),X6091)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_644_zero__less__mult__pos2])])]) ).

fof(i_0_1971,plain,
    ! [X6087,X6088,X6089] :
      ( ~ linord20386208strict(X6087)
      | ~ hBOOL(hAPP(X6087,bool,hAPP(X6087,fun(X6087,bool),ord_less(X6087),zero_zero(X6087)),hAPP(X6087,X6087,hAPP(X6087,fun(X6087,X6087),times_times(X6087),X6088),X6089)))
      | ~ hBOOL(hAPP(X6087,bool,hAPP(X6087,fun(X6087,bool),ord_less(X6087),zero_zero(X6087)),X6088))
      | hBOOL(hAPP(X6087,bool,hAPP(X6087,fun(X6087,bool),ord_less(X6087),zero_zero(X6087)),X6089)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_643_zero__less__mult__pos])])]) ).

fof(i_0_1972,plain,
    ! [X5806,X5807,X5808,X5809,X5810,X5811,X5812] :
      ( ~ hBOOL(hAPP(fun(X5808,bool),bool,hAPP(X5808,fun(fun(X5808,bool),bool),member(X5808),X5811),X5812))
      | hAPP(X5808,X5806,hAPP(fun(X5808,X5807),fun(X5808,X5806),hAPP(fun(X5807,X5806),fun(fun(X5808,X5807),fun(X5808,X5806)),hAPP(fun(X5808,bool),fun(fun(X5807,X5806),fun(fun(X5808,X5807),fun(X5808,X5806))),compose(X5808,X5807,X5806),X5812),X5809),X5810),X5811) = hAPP(X5807,X5806,X5809,hAPP(X5808,X5807,X5810,X5811)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_563_compose__eq])]) ).

fof(i_0_1973,plain,
    ! [X7091,X7092,X7093,X7094] : hAPP(fun(X7091,bool),fun(X7091,bool),hAPP(fun(X7091,bool),fun(fun(X7091,bool),fun(X7091,bool)),semilattice_sup_sup(fun(X7091,bool)),X7092),hAPP(fun(X7091,bool),fun(X7091,bool),hAPP(fun(X7091,bool),fun(fun(X7091,bool),fun(X7091,bool)),semilattice_inf_inf(fun(X7091,bool)),X7093),X7094)) = hAPP(fun(X7091,bool),fun(X7091,bool),hAPP(fun(X7091,bool),fun(fun(X7091,bool),fun(X7091,bool)),semilattice_inf_inf(fun(X7091,bool)),hAPP(fun(X7091,bool),fun(X7091,bool),hAPP(fun(X7091,bool),fun(fun(X7091,bool),fun(X7091,bool)),semilattice_sup_sup(fun(X7091,bool)),X7092),X7093)),hAPP(fun(X7091,bool),fun(X7091,bool),hAPP(fun(X7091,bool),fun(fun(X7091,bool),fun(X7091,bool)),semilattice_sup_sup(fun(X7091,bool)),X7092),X7094)),
    inference(variable_rename,[status(thm)],[fact_883_Un__Int__distrib]) ).

fof(i_0_1974,plain,
    ! [X7087,X7088,X7089,X7090] : hAPP(fun(X7087,bool),fun(X7087,bool),hAPP(fun(X7087,bool),fun(fun(X7087,bool),fun(X7087,bool)),semilattice_inf_inf(fun(X7087,bool)),X7088),hAPP(fun(X7087,bool),fun(X7087,bool),hAPP(fun(X7087,bool),fun(fun(X7087,bool),fun(X7087,bool)),semilattice_sup_sup(fun(X7087,bool)),X7089),X7090)) = hAPP(fun(X7087,bool),fun(X7087,bool),hAPP(fun(X7087,bool),fun(fun(X7087,bool),fun(X7087,bool)),semilattice_sup_sup(fun(X7087,bool)),hAPP(fun(X7087,bool),fun(X7087,bool),hAPP(fun(X7087,bool),fun(fun(X7087,bool),fun(X7087,bool)),semilattice_inf_inf(fun(X7087,bool)),X7088),X7089)),hAPP(fun(X7087,bool),fun(X7087,bool),hAPP(fun(X7087,bool),fun(fun(X7087,bool),fun(X7087,bool)),semilattice_inf_inf(fun(X7087,bool)),X7088),X7090)),
    inference(variable_rename,[status(thm)],[fact_882_Int__Un__distrib]) ).

fof(i_0_1975,plain,
    ! [X5437,X5438,X5439,X5440] :
      ( ~ hBOOL(hAPP(fun(X5437,bool),bool,finite_finite_1(X5437),hAPP(fun(X5438,bool),fun(X5437,bool),hAPP(fun(X5438,X5437),fun(fun(X5438,bool),fun(X5437,bool)),image(X5438,X5437),X5439),X5440)))
      | ~ hBOOL(hAPP(fun(X5438,bool),bool,hAPP(fun(X5438,X5437),fun(fun(X5438,bool),bool),inj_on(X5438,X5437),X5439),X5440))
      | hBOOL(hAPP(fun(X5438,bool),bool,finite_finite_1(X5438),X5440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_479_finite__imageD])]) ).

fof(i_0_1976,plain,
    ! [X4729,X4730] : 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)),X4729)),X4730)),
    inference(variable_rename,[status(thm)],[fact_232_inj__on__add__nat]) ).

cnf(i_0_1977,plain,
    ( 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)),the_inv_into(X1,X2),X4),X3)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) = ti(fun(X1,bool),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_1253]) ).

fof(i_0_1978,plain,
    ! [X7212,X7213,X7214] : hBOOL(hAPP(fun(X7212,bool),bool,hAPP(fun(X7212,bool),fun(fun(X7212,bool),bool),ord_less_eq(fun(X7212,bool)),hAPP(fun(X7212,bool),fun(X7212,bool),hAPP(fun(X7212,bool),fun(fun(X7212,bool),fun(X7212,bool)),semilattice_inf_inf(fun(X7212,bool)),X7213),X7214)),X7213)),
    inference(variable_rename,[status(thm)],[fact_914_Int__lower1]) ).

fof(i_0_1979,plain,
    ! [X7209,X7210,X7211] : hBOOL(hAPP(fun(X7209,bool),bool,hAPP(fun(X7209,bool),fun(fun(X7209,bool),bool),ord_less_eq(fun(X7209,bool)),hAPP(fun(X7209,bool),fun(X7209,bool),hAPP(fun(X7209,bool),fun(fun(X7209,bool),fun(X7209,bool)),semilattice_inf_inf(fun(X7209,bool)),X7210),X7211)),X7211)),
    inference(variable_rename,[status(thm)],[fact_913_Int__lower2]) ).

fof(i_0_1980,plain,
    ! [X6701,X6702,X6703,X6704,X6705] : hAPP(fun(X6701,bool),fun(X6702,bool),hAPP(fun(X6701,X6702),fun(fun(X6701,bool),fun(X6702,bool)),image(X6701,X6702),X6703),hAPP(fun(X6701,bool),fun(X6701,bool),hAPP(fun(X6701,bool),fun(fun(X6701,bool),fun(X6701,bool)),semilattice_sup_sup(fun(X6701,bool)),X6704),X6705)) = hAPP(fun(X6702,bool),fun(X6702,bool),hAPP(fun(X6702,bool),fun(fun(X6702,bool),fun(X6702,bool)),semilattice_sup_sup(fun(X6702,bool)),hAPP(fun(X6701,bool),fun(X6702,bool),hAPP(fun(X6701,X6702),fun(fun(X6701,bool),fun(X6702,bool)),image(X6701,X6702),X6703),X6704)),hAPP(fun(X6701,bool),fun(X6702,bool),hAPP(fun(X6701,X6702),fun(fun(X6701,bool),fun(X6702,bool)),image(X6701,X6702),X6703),X6705)),
    inference(variable_rename,[status(thm)],[fact_781_image__Un]) ).

fof(i_0_1981,plain,
    ! [X4904] : 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)),X4904)))),
    inference(variable_rename,[status(thm)],[fact_283_finite__Collect__le__nat]) ).

fof(i_0_1982,plain,
    ! [X4908] : 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)),X4908)))),
    inference(variable_rename,[status(thm)],[fact_285_finite__Collect__less__nat]) ).

cnf(i_0_1983,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1254]) ).

cnf(i_0_1984,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ti(fun(X1,bool),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1255]) ).

fof(i_0_1985,plain,
    ! [X5932,X5933,X5934,X5935,X5936] :
      ( ~ comm_semiring_1(X5932)
      | hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),X5933),X5934)),hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),X5935),X5936)) = hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),X5933),X5935)),hAPP(X5932,X5932,hAPP(X5932,fun(X5932,X5932),times_times(X5932),X5934),X5936)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])]) ).

fof(i_0_1986,plain,
    ! [X5308,X5309,X5310,X5311,X5312] :
      ( ~ comm_semiring_1(X5308)
      | hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),X5309),X5310)),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),X5311),X5312)) = hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),X5309),X5311)),hAPP(X5308,X5308,hAPP(X5308,fun(X5308,X5308),plus_plus(X5308),X5310),X5312)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_451_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])]) ).

fof(i_0_1987,plain,
    ! [X5922,X5923,X5924,X5925,X5926] :
      ( ~ comm_semiring_1(X5922)
      | hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),X5923),X5924)),hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),X5925),X5926)) = hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),X5923),hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),X5924),hAPP(X5922,X5922,hAPP(X5922,fun(X5922,X5922),times_times(X5922),X5925),X5926))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])])]) ).

cnf(i_0_1988,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk116_4(X1,X3,X2,X4))
    | ~ 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))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1256]) ).

fof(i_0_1989,plain,
    ! [X5385,X5386,X5387,X5388,X5389] :
      ( ~ hBOOL(hAPP(fun(X5386,bool),bool,hAPP(X5386,fun(fun(X5386,bool),bool),member(X5386),X5388),X5389))
      | hBOOL(hAPP(fun(X5385,bool),bool,hAPP(X5385,fun(fun(X5385,bool),bool),member(X5385),hAPP(X5386,X5385,X5387,X5388)),hAPP(fun(X5386,bool),fun(X5385,bool),hAPP(fun(X5386,X5385),fun(fun(X5386,bool),fun(X5385,bool)),image(X5386,X5385),X5387),X5389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_imageI])]) ).

cnf(i_0_1990,plain,
    ( 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))
    | hAPP(X1,X2,X3,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),esk106_3(X1,X2,X3))) != ti(X2,esk106_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1257]) ).

fof(i_0_1991,plain,
    ! [X5866] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5866),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5866),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5866),X5866)))),
    inference(variable_rename,[status(thm)],[fact_573_le__cube]) ).

fof(i_0_1992,plain,
    ! [X6626,X6627,X6628,X6630,X6631,X6632] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk162_2(X6626,X6627)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6627)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6628),X6627))
        | ~ hBOOL(hAPP(nat,bool,X6626,X6628)) )
      & ( hBOOL(hAPP(nat,bool,X6626,esk162_2(X6626,X6627)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6628),X6627))
        | ~ hBOOL(hAPP(nat,bool,X6626,X6628)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk163_2(X6630,X6631)),X6631))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6632),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6631)))
        | ~ hBOOL(hAPP(nat,bool,X6630,X6632)) )
      & ( hBOOL(hAPP(nat,bool,X6630,esk163_2(X6630,X6631)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6632),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6631)))
        | ~ hBOOL(hAPP(nat,bool,X6630,X6632)) ) ),
    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_764_ex__nat__less])])])])])]) ).

fof(i_0_1993,plain,
    ! [X5619,X5620,X5621,X5623,X5624,X5625] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk114_2(X5619,X5620)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5620)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5621),X5620))
        | ~ hBOOL(hAPP(nat,bool,X5619,X5621)) )
      & ( hBOOL(hAPP(nat,bool,X5619,esk114_2(X5619,X5620)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5621),X5620))
        | ~ hBOOL(hAPP(nat,bool,X5619,X5621)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk115_2(X5623,X5624)),X5624))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X5625),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5624)))
        | ~ hBOOL(hAPP(nat,bool,X5623,X5625)) )
      & ( hBOOL(hAPP(nat,bool,X5623,esk115_2(X5623,X5624)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X5625),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5624)))
        | ~ hBOOL(hAPP(nat,bool,X5623,X5625)) ) ),
    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_519_ex__nat__less__eq])])])])])]) ).

fof(i_0_1994,plain,
    ! [X6007,X6008,X6009] :
      ( ( hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6008),zero_zero(X6007)))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6008))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) )
      & ( hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6009),zero_zero(X6007)))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6008))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) )
      & ( hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6008),zero_zero(X6007)))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6009))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) )
      & ( hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6009),zero_zero(X6007)))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6009))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) )
      & ( ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6008))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),X6009))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) )
      & ( ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6008),zero_zero(X6007)))
        | ~ hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),X6009),zero_zero(X6007)))
        | hBOOL(hAPP(X6007,bool,hAPP(X6007,fun(X6007,bool),ord_less_eq(X6007),zero_zero(X6007)),hAPP(X6007,X6007,hAPP(X6007,fun(X6007,X6007),times_times(X6007),X6008),X6009)))
        | ~ linord581940658strict(X6007) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_620_zero__le__mult__iff])])])]) ).

fof(i_0_1995,plain,
    ! [X7423,X7424,X7425,X7426] :
      ( ( ~ hBOOL(hAPP(fun(X7423,bool),bool,finite_finite_1(X7423),X7426))
        | hAPP(fun(X7423,bool),X7424,hAPP(fun(X7423,X7424),fun(fun(X7423,bool),X7424),big_co1399186613setsum(X7423,X7424),X7425),X7426) = hAPP(fun(X7423,bool),X7424,hAPP(X7424,fun(fun(X7423,bool),X7424),hAPP(fun(X7423,X7424),fun(X7424,fun(fun(X7423,bool),X7424)),hAPP(fun(X7424,fun(X7424,X7424)),fun(fun(X7423,X7424),fun(X7424,fun(fun(X7423,bool),X7424))),finite_fold_image(X7424,X7423),plus_plus(X7424)),X7425),zero_zero(X7424)),X7426)
        | ~ comm_monoid_add(X7424) )
      & ( hBOOL(hAPP(fun(X7423,bool),bool,finite_finite_1(X7423),X7426))
        | hAPP(fun(X7423,bool),X7424,hAPP(fun(X7423,X7424),fun(fun(X7423,bool),X7424),big_co1399186613setsum(X7423,X7424),X7425),X7426) = zero_zero(X7424)
        | ~ comm_monoid_add(X7424) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1258])])])]) ).

fof(i_0_1996,plain,
    ! [X7427,X7428,X7429,X7430] :
      ( ~ comm_monoid_add(X7428)
      | ~ hBOOL(hAPP(fun(X7427,bool),bool,finite_finite_1(X7427),X7430))
      | hAPP(fun(X7427,bool),X7428,hAPP(fun(X7427,X7428),fun(fun(X7427,bool),X7428),big_co1399186613setsum(X7427,X7428),X7429),X7430) = hAPP(fun(X7427,bool),X7428,hAPP(X7428,fun(fun(X7427,bool),X7428),hAPP(fun(X7427,X7428),fun(X7428,fun(fun(X7427,bool),X7428)),hAPP(fun(X7428,fun(X7428,X7428)),fun(fun(X7427,X7428),fun(X7428,fun(fun(X7427,bool),X7428))),finite_fold_image(X7428,X7427),plus_plus(X7428)),X7429),zero_zero(X7428)),X7430) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_971_setsum_Oeq__fold])])]) ).

fof(i_0_1997,plain,
    ! [X6634,X6635,X6637,X6638,X6639,X6641] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk164_2(X6634,X6635)),X6635))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6637),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6635)))
        | hBOOL(hAPP(nat,bool,X6634,X6637)) )
      & ( ~ hBOOL(hAPP(nat,bool,X6634,esk164_2(X6634,X6635)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X6637),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6635)))
        | hBOOL(hAPP(nat,bool,X6634,X6637)) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk165_2(X6638,X6639)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X6639)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6641),X6639))
        | hBOOL(hAPP(nat,bool,X6638,X6641)) )
      & ( ~ hBOOL(hAPP(nat,bool,X6638,esk165_2(X6638,X6639)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X6641),X6639))
        | hBOOL(hAPP(nat,bool,X6638,X6641)) ) ),
    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_765_all__nat__less])])])])])]) ).

fof(i_0_1998,plain,
    ! [X5611,X5612,X5614,X5615,X5616,X5618] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk112_2(X5611,X5612)),X5612))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X5614),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5612)))
        | hBOOL(hAPP(nat,bool,X5611,X5614)) )
      & ( ~ hBOOL(hAPP(nat,bool,X5611,esk112_2(X5611,X5612)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X5614),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5612)))
        | hBOOL(hAPP(nat,bool,X5611,X5614)) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk113_2(X5615,X5616)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X5616)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5618),X5616))
        | hBOOL(hAPP(nat,bool,X5615,X5618)) )
      & ( ~ hBOOL(hAPP(nat,bool,X5615,esk113_2(X5615,X5616)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5618),X5616))
        | hBOOL(hAPP(nat,bool,X5615,X5618)) ) ),
    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_518_all__nat__less__eq])])])])])]) ).

fof(i_0_1999,plain,
    ! [X7266,X7267,X7268,X7269] :
      ( ~ semilattice_inf(X7266)
      | ~ hBOOL(hAPP(X7266,bool,hAPP(X7266,fun(X7266,bool),ord_less_eq(X7266),X7268),X7269))
      | hBOOL(hAPP(X7266,bool,hAPP(X7266,fun(X7266,bool),ord_less_eq(X7266),hAPP(X7266,X7266,hAPP(X7266,fun(X7266,X7266),semilattice_inf_inf(X7266),X7268),X7267)),X7269)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_927_le__infI1])])]) ).

fof(i_0_2000,plain,
    ! [X7262,X7263,X7264,X7265] :
      ( ~ semilattice_inf(X7262)
      | ~ hBOOL(hAPP(X7262,bool,hAPP(X7262,fun(X7262,bool),ord_less_eq(X7262),X7264),X7265))
      | hBOOL(hAPP(X7262,bool,hAPP(X7262,fun(X7262,bool),ord_less_eq(X7262),hAPP(X7262,X7262,hAPP(X7262,fun(X7262,X7262),semilattice_inf_inf(X7262),X7263),X7264)),X7265)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_926_le__infI2])])]) ).

fof(i_0_2001,plain,
    ! [X7352,X7353,X7354,X7355] :
      ( ~ semilattice_inf(X7352)
      | ~ hBOOL(hAPP(X7352,bool,hAPP(X7352,fun(X7352,bool),ord_less(X7352),X7354),X7355))
      | hBOOL(hAPP(X7352,bool,hAPP(X7352,fun(X7352,bool),ord_less(X7352),hAPP(X7352,X7352,hAPP(X7352,fun(X7352,X7352),semilattice_inf_inf(X7352),X7354),X7353)),X7355)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_953_less__infI1])])]) ).

fof(i_0_2002,plain,
    ! [X7356,X7357,X7358,X7359] :
      ( ~ semilattice_inf(X7356)
      | ~ hBOOL(hAPP(X7356,bool,hAPP(X7356,fun(X7356,bool),ord_less(X7356),X7358),X7359))
      | hBOOL(hAPP(X7356,bool,hAPP(X7356,fun(X7356,bool),ord_less(X7356),hAPP(X7356,X7356,hAPP(X7356,fun(X7356,X7356),semilattice_inf_inf(X7356),X7357),X7358)),X7359)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_954_less__infI2])])]) ).

fof(i_0_2003,plain,
    ! [X6427,X6428,X6429,X6430,X6431,X6432,X6433] : hAPP(fun(X6427,X6428),fun(X6427,X6429),hAPP(fun(X6428,X6429),fun(fun(X6427,X6428),fun(X6427,X6429)),comp(X6428,X6429,X6427),X6431),hAPP(fun(X6427,X6430),fun(X6427,X6428),hAPP(fun(X6430,X6428),fun(fun(X6427,X6430),fun(X6427,X6428)),comp(X6430,X6428,X6427),X6432),X6433)) = hAPP(fun(X6427,X6430),fun(X6427,X6429),hAPP(fun(X6430,X6429),fun(fun(X6427,X6430),fun(X6427,X6429)),comp(X6430,X6429,X6427),hAPP(fun(X6430,X6428),fun(X6430,X6429),hAPP(fun(X6428,X6429),fun(fun(X6430,X6428),fun(X6430,X6429)),comp(X6428,X6429,X6430),X6431),X6432)),X6433),
    inference(variable_rename,[status(thm)],[fact_729_o__assoc]) ).

fof(i_0_2004,plain,
    ! [X5088,X5089] :
      ( ( ~ 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),X5088),X5089)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5088))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5089)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5088))
        | 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),X5088),X5089))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5089))
        | 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),X5088),X5089))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_356_add__gr__0])])]) ).

fof(i_0_2005,plain,
    ! [X4983,X4984,X4985,X4986] :
      ( ( hBOOL(hAPP(fun(X4983,bool),bool,finite_finite_1(X4983),X4985))
        | ~ hBOOL(hAPP(fun(sum_sum(X4983,X4984),bool),bool,finite_finite_1(sum_sum(X4983,X4984)),hAPP(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool),hAPP(fun(X4983,bool),fun(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool)),sum_Plus(X4983,X4984),X4985),X4986))) )
      & ( hBOOL(hAPP(fun(X4984,bool),bool,finite_finite_1(X4984),X4986))
        | ~ hBOOL(hAPP(fun(sum_sum(X4983,X4984),bool),bool,finite_finite_1(sum_sum(X4983,X4984)),hAPP(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool),hAPP(fun(X4983,bool),fun(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool)),sum_Plus(X4983,X4984),X4985),X4986))) )
      & ( ~ hBOOL(hAPP(fun(X4983,bool),bool,finite_finite_1(X4983),X4985))
        | ~ hBOOL(hAPP(fun(X4984,bool),bool,finite_finite_1(X4984),X4986))
        | hBOOL(hAPP(fun(sum_sum(X4983,X4984),bool),bool,finite_finite_1(sum_sum(X4983,X4984)),hAPP(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool),hAPP(fun(X4983,bool),fun(fun(X4984,bool),fun(sum_sum(X4983,X4984),bool)),sum_Plus(X4983,X4984),X4985),X4986))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_311_finite__Plus__iff])])]) ).

fof(i_0_2006,plain,
    ! [X4975,X4976,X4977,X4978] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X4975,X4976),bool),bool,finite_finite_1(sum_sum(X4975,X4976)),hAPP(fun(X4976,bool),fun(sum_sum(X4975,X4976),bool),hAPP(fun(X4975,bool),fun(fun(X4976,bool),fun(sum_sum(X4975,X4976),bool)),sum_Plus(X4975,X4976),X4977),X4978)))
      | hBOOL(hAPP(fun(X4975,bool),bool,finite_finite_1(X4975),X4977)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_309_finite__PlusD_I1_J])]) ).

fof(i_0_2007,plain,
    ! [X4971,X4972,X4973,X4974] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X4971,X4972),bool),bool,finite_finite_1(sum_sum(X4971,X4972)),hAPP(fun(X4972,bool),fun(sum_sum(X4971,X4972),bool),hAPP(fun(X4971,bool),fun(fun(X4972,bool),fun(sum_sum(X4971,X4972),bool)),sum_Plus(X4971,X4972),X4973),X4974)))
      | hBOOL(hAPP(fun(X4972,bool),bool,finite_finite_1(X4972),X4974)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_308_finite__PlusD_I2_J])]) ).

cnf(i_0_2008,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),esk27_2(X1,X2)))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1259]) ).

fof(i_0_2009,plain,
    ! [X5840,X5841,X5842,X5843,X5844,X5845] : hAPP(fun(X5840,X5841),fun(X5840,X5842),hAPP(fun(X5841,X5842),fun(fun(X5840,X5841),fun(X5840,X5842)),hAPP(fun(X5840,bool),fun(fun(X5841,X5842),fun(fun(X5840,X5841),fun(X5840,X5842))),compose(X5840,X5841,X5842),X5843),X5844),X5845) = hAPP(fun(X5840,bool),fun(X5840,X5842),hAPP(fun(X5840,X5842),fun(fun(X5840,bool),fun(X5840,X5842)),restrict(X5840,X5842),hAPP(fun(X5840,X5841),fun(X5840,X5842),hAPP(fun(X5841,X5842),fun(fun(X5840,X5841),fun(X5840,X5842)),combb(X5841,X5842,X5840),X5844),X5845)),X5843),
    inference(variable_rename,[status(thm)],[fact_567_compose__def]) ).

fof(i_0_2010,plain,
    ! [X4800,X4801,X4802,X4803] :
      ( ( hBOOL(hAPP(X4800,bool,hAPP(X4801,fun(X4800,bool),X4803,esk57_4(X4800,X4801,X4802,X4803)),esk58_4(X4800,X4801,X4802,X4803)))
        | hBOOL(hAPP(fun(X4801,fun(X4800,bool)),bool,hAPP(fun(X4801,fun(X4800,bool)),fun(fun(X4801,fun(X4800,bool)),bool),ord_less_eq(fun(X4801,fun(X4800,bool))),X4803),X4802)) )
      & ( ~ hBOOL(hAPP(X4800,bool,hAPP(X4801,fun(X4800,bool),X4802,esk57_4(X4800,X4801,X4802,X4803)),esk58_4(X4800,X4801,X4802,X4803)))
        | hBOOL(hAPP(fun(X4801,fun(X4800,bool)),bool,hAPP(fun(X4801,fun(X4800,bool)),fun(fun(X4801,fun(X4800,bool)),bool),ord_less_eq(fun(X4801,fun(X4800,bool))),X4803),X4802)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_257_predicate2I])])])]) ).

fof(i_0_2011,plain,
    ! [X6381,X6382,X6383,X6384,X6385] :
      ( hAPP(fun(X6382,bool),fun(X6383,bool),hAPP(fun(X6382,X6383),fun(fun(X6382,bool),fun(X6383,bool)),image(X6382,X6383),X6385),top_top(fun(X6382,bool))) != top_top(fun(X6383,bool))
      | hAPP(fun(X6383,bool),fun(X6381,bool),hAPP(fun(X6383,X6381),fun(fun(X6383,bool),fun(X6381,bool)),image(X6383,X6381),X6384),top_top(fun(X6383,bool))) != top_top(fun(X6381,bool))
      | hAPP(fun(X6382,bool),fun(X6381,bool),hAPP(fun(X6382,X6381),fun(fun(X6382,bool),fun(X6381,bool)),image(X6382,X6381),hAPP(fun(X6382,X6383),fun(X6382,X6381),hAPP(fun(X6383,X6381),fun(fun(X6382,X6383),fun(X6382,X6381)),comp(X6383,X6381,X6382),X6384),X6385)),top_top(fun(X6382,bool))) = top_top(fun(X6381,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_720_comp__surj])]) ).

cnf(i_0_2012,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_1260]) ).

cnf(i_0_2013,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_1260]) ).

cnf(i_0_2014,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_1261]) ).

cnf(i_0_2015,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_1262]) ).

cnf(i_0_2016,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_1263]) ).

fof(i_0_2017,plain,
    ! [X5715,X5716,X5717] :
      ( ( ~ hBOOL(hAPP(fun(X5715,bool),bool,hAPP(fun(X5715,bool),fun(fun(X5715,bool),bool),ord_less_eq(fun(X5715,bool)),hAPP(X5715,fun(X5715,bool),ord_greaterThan(X5715),X5716)),hAPP(X5715,fun(X5715,bool),ord_greaterThan(X5715),X5717)))
        | hBOOL(hAPP(X5715,bool,hAPP(X5715,fun(X5715,bool),ord_less_eq(X5715),X5717),X5716))
        | ~ linorder(X5715) )
      & ( ~ hBOOL(hAPP(X5715,bool,hAPP(X5715,fun(X5715,bool),ord_less_eq(X5715),X5717),X5716))
        | hBOOL(hAPP(fun(X5715,bool),bool,hAPP(fun(X5715,bool),fun(fun(X5715,bool),bool),ord_less_eq(fun(X5715,bool)),hAPP(X5715,fun(X5715,bool),ord_greaterThan(X5715),X5716)),hAPP(X5715,fun(X5715,bool),ord_greaterThan(X5715),X5717)))
        | ~ linorder(X5715) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_542_greaterThan__subset__iff])])])]) ).

fof(i_0_2018,plain,
    ! [X7017,X7018,X7019] :
      ( ( ~ hBOOL(hAPP(fun(X7017,bool),bool,hAPP(fun(X7017,bool),fun(fun(X7017,bool),bool),ord_less_eq(fun(X7017,bool)),hAPP(X7017,fun(X7017,bool),ord_atLeast(X7017),X7018)),hAPP(X7017,fun(X7017,bool),ord_atLeast(X7017),X7019)))
        | hBOOL(hAPP(X7017,bool,hAPP(X7017,fun(X7017,bool),ord_less_eq(X7017),X7019),X7018))
        | ~ order(X7017) )
      & ( ~ hBOOL(hAPP(X7017,bool,hAPP(X7017,fun(X7017,bool),ord_less_eq(X7017),X7019),X7018))
        | hBOOL(hAPP(fun(X7017,bool),bool,hAPP(fun(X7017,bool),fun(fun(X7017,bool),bool),ord_less_eq(fun(X7017,bool)),hAPP(X7017,fun(X7017,bool),ord_atLeast(X7017),X7018)),hAPP(X7017,fun(X7017,bool),ord_atLeast(X7017),X7019)))
        | ~ order(X7017) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_862_atLeast__subset__iff])])])]) ).

cnf(i_0_2019,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_1264]) ).

cnf(i_0_2020,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_1265]) ).

cnf(i_0_2021,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_1244]) ).

fof(i_0_2022,plain,
    ! [X6058,X6059,X6060] :
      ( ( ~ hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),zero_zero(X6058)),X6060))
        | ~ hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),zero_zero(X6058)),X6059))
        | hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),zero_zero(X6058)),hAPP(X6058,X6058,hAPP(X6058,fun(X6058,X6058),times_times(X6058),X6060),X6059)))
        | ~ ordered_ring(X6058) )
      & ( ~ hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),X6060),zero_zero(X6058)))
        | ~ hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),X6059),zero_zero(X6058)))
        | hBOOL(hAPP(X6058,bool,hAPP(X6058,fun(X6058,bool),ord_less_eq(X6058),zero_zero(X6058)),hAPP(X6058,X6058,hAPP(X6058,fun(X6058,X6058),times_times(X6058),X6060),X6059)))
        | ~ ordered_ring(X6058) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_634_split__mult__pos__le])])])]) ).

fof(i_0_2023,plain,
    ! [X6013,X6014,X6015] :
      ( ~ ordere453448008miring(X6013)
      | ~ hBOOL(hAPP(X6013,bool,hAPP(X6013,fun(X6013,bool),ord_less_eq(X6013),zero_zero(X6013)),X6015))
      | ~ hBOOL(hAPP(X6013,bool,hAPP(X6013,fun(X6013,bool),ord_less_eq(X6013),zero_zero(X6013)),X6014))
      | hBOOL(hAPP(X6013,bool,hAPP(X6013,fun(X6013,bool),ord_less_eq(X6013),zero_zero(X6013)),hAPP(X6013,X6013,hAPP(X6013,fun(X6013,X6013),times_times(X6013),X6015),X6014))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_622_mult__nonneg__nonneg])])]) ).

fof(i_0_2024,plain,
    ! [X5063,X5064,X5065] :
      ( ~ ordere216010020id_add(X5063)
      | ~ hBOOL(hAPP(X5063,bool,hAPP(X5063,fun(X5063,bool),ord_less_eq(X5063),zero_zero(X5063)),X5065))
      | ~ hBOOL(hAPP(X5063,bool,hAPP(X5063,fun(X5063,bool),ord_less_eq(X5063),zero_zero(X5063)),X5064))
      | hBOOL(hAPP(X5063,bool,hAPP(X5063,fun(X5063,bool),ord_less_eq(X5063),zero_zero(X5063)),hAPP(X5063,X5063,hAPP(X5063,fun(X5063,X5063),plus_plus(X5063),X5065),X5064))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_344_add__nonneg__nonneg])])]) ).

fof(i_0_2025,plain,
    ! [X6078,X6079,X6080] :
      ( ~ linord20386208strict(X6078)
      | ~ hBOOL(hAPP(X6078,bool,hAPP(X6078,fun(X6078,bool),ord_less(X6078),zero_zero(X6078)),X6080))
      | ~ hBOOL(hAPP(X6078,bool,hAPP(X6078,fun(X6078,bool),ord_less(X6078),zero_zero(X6078)),X6079))
      | hBOOL(hAPP(X6078,bool,hAPP(X6078,fun(X6078,bool),ord_less(X6078),zero_zero(X6078)),hAPP(X6078,X6078,hAPP(X6078,fun(X6078,X6078),times_times(X6078),X6080),X6079))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_640_mult__pos__pos])])]) ).

fof(i_0_2026,plain,
    ! [X5109,X5110,X5111] :
      ( ~ ordere216010020id_add(X5109)
      | ~ hBOOL(hAPP(X5109,bool,hAPP(X5109,fun(X5109,bool),ord_less(X5109),zero_zero(X5109)),X5111))
      | ~ hBOOL(hAPP(X5109,bool,hAPP(X5109,fun(X5109,bool),ord_less_eq(X5109),zero_zero(X5109)),X5110))
      | hBOOL(hAPP(X5109,bool,hAPP(X5109,fun(X5109,bool),ord_less(X5109),zero_zero(X5109)),hAPP(X5109,X5109,hAPP(X5109,fun(X5109,X5109),plus_plus(X5109),X5111),X5110))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_363_add__pos__nonneg])])]) ).

fof(i_0_2027,plain,
    ! [X5106,X5107,X5108] :
      ( ~ ordere216010020id_add(X5106)
      | ~ hBOOL(hAPP(X5106,bool,hAPP(X5106,fun(X5106,bool),ord_less_eq(X5106),zero_zero(X5106)),X5108))
      | ~ hBOOL(hAPP(X5106,bool,hAPP(X5106,fun(X5106,bool),ord_less(X5106),zero_zero(X5106)),X5107))
      | hBOOL(hAPP(X5106,bool,hAPP(X5106,fun(X5106,bool),ord_less(X5106),zero_zero(X5106)),hAPP(X5106,X5106,hAPP(X5106,fun(X5106,X5106),plus_plus(X5106),X5108),X5107))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_add__nonneg__pos])])]) ).

fof(i_0_2028,plain,
    ! [X5077,X5078,X5079] :
      ( ~ ordere216010020id_add(X5077)
      | ~ hBOOL(hAPP(X5077,bool,hAPP(X5077,fun(X5077,bool),ord_less(X5077),zero_zero(X5077)),X5079))
      | ~ hBOOL(hAPP(X5077,bool,hAPP(X5077,fun(X5077,bool),ord_less(X5077),zero_zero(X5077)),X5078))
      | hBOOL(hAPP(X5077,bool,hAPP(X5077,fun(X5077,bool),ord_less(X5077),zero_zero(X5077)),hAPP(X5077,X5077,hAPP(X5077,fun(X5077,X5077),plus_plus(X5077),X5079),X5078))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_add__pos__pos])])]) ).

fof(i_0_2029,plain,
    ! [X6132,X6133,X6134] :
      ( ~ linordered_semidom(X6132)
      | ~ hBOOL(hAPP(X6132,bool,hAPP(X6132,fun(X6132,bool),ord_less(X6132),one_one(X6132)),X6134))
      | ~ hBOOL(hAPP(X6132,bool,hAPP(X6132,fun(X6132,bool),ord_less(X6132),one_one(X6132)),X6133))
      | hBOOL(hAPP(X6132,bool,hAPP(X6132,fun(X6132,bool),ord_less(X6132),one_one(X6132)),hAPP(X6132,X6132,hAPP(X6132,fun(X6132,X6132),times_times(X6132),X6134),X6133))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_655_less__1__mult])])]) ).

fof(i_0_2030,plain,
    ! [X5427,X5428,X5429,X5430,X5431] : hAPP(fun(X5427,bool),fun(X5428,bool),hAPP(fun(X5427,X5428),fun(fun(X5427,bool),fun(X5428,bool)),image(X5427,X5428),hAPP(fun(X5427,X5429),fun(X5427,X5428),hAPP(fun(X5429,X5428),fun(fun(X5427,X5429),fun(X5427,X5428)),combb(X5429,X5428,X5427),X5430),X5431)),top_top(fun(X5427,bool))) = hAPP(fun(X5429,bool),fun(X5428,bool),hAPP(fun(X5429,X5428),fun(fun(X5429,bool),fun(X5428,bool)),image(X5429,X5428),X5430),hAPP(fun(X5427,bool),fun(X5429,bool),hAPP(fun(X5427,X5429),fun(fun(X5427,bool),fun(X5429,bool)),image(X5427,X5429),X5431),top_top(fun(X5427,bool)))),
    inference(variable_rename,[status(thm)],[fact_477_range__composition]) ).

fof(i_0_2031,plain,
    ! [X6025,X6026,X6027] :
      ( ~ ordered_ring(X6025)
      | ~ hBOOL(hAPP(X6025,bool,hAPP(X6025,fun(X6025,bool),ord_less_eq(X6025),X6027),zero_zero(X6025)))
      | ~ hBOOL(hAPP(X6025,bool,hAPP(X6025,fun(X6025,bool),ord_less_eq(X6025),X6026),zero_zero(X6025)))
      | hBOOL(hAPP(X6025,bool,hAPP(X6025,fun(X6025,bool),ord_less_eq(X6025),zero_zero(X6025)),hAPP(X6025,X6025,hAPP(X6025,fun(X6025,X6025),times_times(X6025),X6027),X6026))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_626_mult__nonpos__nonpos])])]) ).

fof(i_0_2032,plain,
    ! [X6100,X6101,X6102] :
      ( ~ linord581940658strict(X6100)
      | ~ hBOOL(hAPP(X6100,bool,hAPP(X6100,fun(X6100,bool),ord_less(X6100),X6102),zero_zero(X6100)))
      | ~ hBOOL(hAPP(X6100,bool,hAPP(X6100,fun(X6100,bool),ord_less(X6100),X6101),zero_zero(X6100)))
      | hBOOL(hAPP(X6100,bool,hAPP(X6100,fun(X6100,bool),ord_less(X6100),zero_zero(X6100)),hAPP(X6100,X6100,hAPP(X6100,fun(X6100,X6100),times_times(X6100),X6102),X6101))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_647_mult__neg__neg])])]) ).

fof(i_0_2033,plain,
    ! [X5056,X5057,X5058,X5059] :
      ( ~ ordere216010020id_add(X5056)
      | ~ hBOOL(hAPP(X5056,bool,hAPP(X5056,fun(X5056,bool),ord_less_eq(X5056),zero_zero(X5056)),X5059))
      | ~ hBOOL(hAPP(X5056,bool,hAPP(X5056,fun(X5056,bool),ord_less_eq(X5056),X5057),X5058))
      | hBOOL(hAPP(X5056,bool,hAPP(X5056,fun(X5056,bool),ord_less_eq(X5056),X5057),hAPP(X5056,X5056,hAPP(X5056,fun(X5056,X5056),plus_plus(X5056),X5059),X5058))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_342_add__increasing])])]) ).

fof(i_0_2034,plain,
    ! [X5052,X5053,X5054,X5055] :
      ( ~ ordere216010020id_add(X5052)
      | ~ hBOOL(hAPP(X5052,bool,hAPP(X5052,fun(X5052,bool),ord_less_eq(X5052),zero_zero(X5052)),X5055))
      | ~ hBOOL(hAPP(X5052,bool,hAPP(X5052,fun(X5052,bool),ord_less_eq(X5052),X5053),X5054))
      | hBOOL(hAPP(X5052,bool,hAPP(X5052,fun(X5052,bool),ord_less_eq(X5052),X5053),hAPP(X5052,X5052,hAPP(X5052,fun(X5052,X5052),plus_plus(X5052),X5054),X5055))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_add__increasing2])])]) ).

fof(i_0_2035,plain,
    ! [X5102,X5103,X5104,X5105] :
      ( ~ ordere216010020id_add(X5102)
      | ~ hBOOL(hAPP(X5102,bool,hAPP(X5102,fun(X5102,bool),ord_less(X5102),zero_zero(X5102)),X5105))
      | ~ hBOOL(hAPP(X5102,bool,hAPP(X5102,fun(X5102,bool),ord_less_eq(X5102),X5103),X5104))
      | hBOOL(hAPP(X5102,bool,hAPP(X5102,fun(X5102,bool),ord_less(X5102),X5103),hAPP(X5102,X5102,hAPP(X5102,fun(X5102,X5102),plus_plus(X5102),X5105),X5104))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_add__strict__increasing])])]) ).

fof(i_0_2036,plain,
    ! [X5098,X5099,X5100,X5101] :
      ( ~ ordere216010020id_add(X5098)
      | ~ hBOOL(hAPP(X5098,bool,hAPP(X5098,fun(X5098,bool),ord_less_eq(X5098),zero_zero(X5098)),X5101))
      | ~ hBOOL(hAPP(X5098,bool,hAPP(X5098,fun(X5098,bool),ord_less(X5098),X5099),X5100))
      | hBOOL(hAPP(X5098,bool,hAPP(X5098,fun(X5098,bool),ord_less(X5098),X5099),hAPP(X5098,X5098,hAPP(X5098,fun(X5098,X5098),plus_plus(X5098),X5101),X5100))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_360_add__strict__increasing2])])]) ).

fof(i_0_2037,plain,
    ! [X5073,X5074,X5075,X5076] :
      ( ~ linordered_semidom(X5073)
      | ~ hBOOL(hAPP(X5073,bool,hAPP(X5073,fun(X5073,bool),ord_less(X5073),zero_zero(X5073)),X5076))
      | ~ hBOOL(hAPP(X5073,bool,hAPP(X5073,fun(X5073,bool),ord_less(X5073),X5074),X5075))
      | hBOOL(hAPP(X5073,bool,hAPP(X5073,fun(X5073,bool),ord_less(X5073),X5074),hAPP(X5073,X5073,hAPP(X5073,fun(X5073,X5073),plus_plus(X5073),X5076),X5075))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_pos__add__strict])])]) ).

fof(i_0_2038,plain,
    ! [X7270,X7271,X7272,X7273] :
      ( ( hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),X7272))
        | ~ hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),hAPP(X7270,X7270,hAPP(X7270,fun(X7270,X7270),semilattice_inf_inf(X7270),X7272),X7273)))
        | ~ semilattice_inf(X7270) )
      & ( hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),X7273))
        | ~ hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),hAPP(X7270,X7270,hAPP(X7270,fun(X7270,X7270),semilattice_inf_inf(X7270),X7272),X7273)))
        | ~ semilattice_inf(X7270) )
      & ( ~ hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),X7272))
        | ~ hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),X7273))
        | hBOOL(hAPP(X7270,bool,hAPP(X7270,fun(X7270,bool),ord_less_eq(X7270),X7271),hAPP(X7270,X7270,hAPP(X7270,fun(X7270,X7270),semilattice_inf_inf(X7270),X7272),X7273)))
        | ~ semilattice_inf(X7270) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_928_le__inf__iff])])])]) ).

fof(i_0_2039,plain,
    ! [X7252,X7253,X7254,X7255] :
      ( ~ semilattice_inf(X7252)
      | ~ hBOOL(hAPP(X7252,bool,hAPP(X7252,fun(X7252,bool),ord_less_eq(X7252),X7254),X7255))
      | ~ hBOOL(hAPP(X7252,bool,hAPP(X7252,fun(X7252,bool),ord_less_eq(X7252),X7254),X7253))
      | hBOOL(hAPP(X7252,bool,hAPP(X7252,fun(X7252,bool),ord_less_eq(X7252),X7254),hAPP(X7252,X7252,hAPP(X7252,fun(X7252,X7252),semilattice_inf_inf(X7252),X7255),X7253))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_923_le__infI])])]) ).

fof(i_0_2040,plain,
    ! [X7248,X7249,X7250,X7251] :
      ( ~ semilattice_inf(X7248)
      | ~ hBOOL(hAPP(X7248,bool,hAPP(X7248,fun(X7248,bool),ord_less_eq(X7248),X7250),X7251))
      | ~ hBOOL(hAPP(X7248,bool,hAPP(X7248,fun(X7248,bool),ord_less_eq(X7248),X7250),X7249))
      | hBOOL(hAPP(X7248,bool,hAPP(X7248,fun(X7248,bool),ord_less_eq(X7248),X7250),hAPP(X7248,X7248,hAPP(X7248,fun(X7248,X7248),semilattice_inf_inf(X7248),X7251),X7249))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_922_inf__greatest])])]) ).

fof(i_0_2041,plain,
    ! [X5318,X5319,X5320] :
      ( ( hBOOL(hAPP(X5318,bool,hAPP(X5318,fun(X5318,bool),ord_less(X5318),zero_zero(X5318)),esk100_3(X5318,X5319,X5320)))
        | hBOOL(hAPP(X5318,bool,hAPP(X5318,fun(X5318,bool),ord_less_eq(X5318),X5319),X5320))
        | ~ linordered_field(X5318) )
      & ( ~ hBOOL(hAPP(X5318,bool,hAPP(X5318,fun(X5318,bool),ord_less_eq(X5318),X5319),hAPP(X5318,X5318,hAPP(X5318,fun(X5318,X5318),plus_plus(X5318),X5320),esk100_3(X5318,X5319,X5320))))
        | hBOOL(hAPP(X5318,bool,hAPP(X5318,fun(X5318,bool),ord_less_eq(X5318),X5319),X5320))
        | ~ linordered_field(X5318) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_field__le__epsilon])])])])]) ).

fof(i_0_2042,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),esk20_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk20_0),arrow_1568854078le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1266])])]) ).

fof(i_0_2043,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),esk19_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk19_0),arrow_1568854078le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1267])])]) ).

fof(i_0_2044,plain,
    ! [X5367,X5368,X5369,X5370,X5371,X5372] : hAPP(fun(X5367,bool),fun(X5368,bool),hAPP(fun(X5367,X5368),fun(fun(X5367,bool),fun(X5368,bool)),image(X5367,X5368),X5370),hAPP(fun(X5369,bool),fun(X5367,bool),hAPP(fun(X5369,X5367),fun(fun(X5369,bool),fun(X5367,bool)),image(X5369,X5367),X5371),X5372)) = hAPP(fun(X5369,bool),fun(X5368,bool),hAPP(fun(X5369,X5368),fun(fun(X5369,bool),fun(X5368,bool)),image(X5369,X5368),hAPP(fun(X5369,X5367),fun(X5369,X5368),hAPP(fun(X5367,X5368),fun(fun(X5369,X5367),fun(X5369,X5368)),combb(X5367,X5368,X5369),X5370),X5371)),X5372),
    inference(variable_rename,[status(thm)],[fact_467_image__image]) ).

fof(i_0_2045,plain,
    ! [X6409,X6410,X6411,X6412,X6413,X6414] : hAPP(fun(X6409,bool),fun(X6410,bool),hAPP(fun(X6409,X6410),fun(fun(X6409,bool),fun(X6410,bool)),image(X6409,X6410),hAPP(fun(X6409,X6411),fun(X6409,X6410),hAPP(fun(X6411,X6410),fun(fun(X6409,X6411),fun(X6409,X6410)),comp(X6411,X6410,X6409),X6412),X6413)),X6414) = hAPP(fun(X6411,bool),fun(X6410,bool),hAPP(fun(X6411,X6410),fun(fun(X6411,bool),fun(X6410,bool)),image(X6411,X6410),X6412),hAPP(fun(X6409,bool),fun(X6411,bool),hAPP(fun(X6409,X6411),fun(fun(X6409,bool),fun(X6411,bool)),image(X6409,X6411),X6413),X6414)),
    inference(variable_rename,[status(thm)],[fact_725_image__compose]) ).

fof(i_0_2046,plain,
    ! [X4431,X4432,X4433,X4434] :
      ( ( hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),X4433),esk38_4(X4431,X4432,X4433,X4434)))
        | hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less_eq(X4431),X4434),X4432))
        | ~ hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),X4433),X4434))
        | ~ dense_linorder(X4431) )
      & ( hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),esk38_4(X4431,X4432,X4433,X4434)),X4434))
        | hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less_eq(X4431),X4434),X4432))
        | ~ hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),X4433),X4434))
        | ~ dense_linorder(X4431) )
      & ( ~ hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less_eq(X4431),esk38_4(X4431,X4432,X4433,X4434)),X4432))
        | hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less_eq(X4431),X4434),X4432))
        | ~ hBOOL(hAPP(X4431,bool,hAPP(X4431,fun(X4431,bool),ord_less(X4431),X4433),X4434))
        | ~ dense_linorder(X4431) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_dense__le__bounded])])])])]) ).

fof(i_0_2047,plain,
    ! [X5882,X5883,X5884,X5885] :
      ( ~ comm_semiring_1(X5882)
      | hAPP(X5882,X5882,hAPP(X5882,fun(X5882,X5882),plus_plus(X5882),hAPP(X5882,X5882,hAPP(X5882,fun(X5882,X5882),times_times(X5882),X5883),X5884)),hAPP(X5882,X5882,hAPP(X5882,fun(X5882,X5882),times_times(X5882),X5885),X5884)) = hAPP(X5882,X5882,hAPP(X5882,fun(X5882,X5882),times_times(X5882),hAPP(X5882,X5882,hAPP(X5882,fun(X5882,X5882),plus_plus(X5882),X5883),X5885)),X5884) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_578_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])])]) ).

fof(i_0_2048,plain,
    ! [X7065,X7066,X7067,X7068] :
      ( ~ distrib_lattice(X7065)
      | hAPP(X7065,X7065,hAPP(X7065,fun(X7065,X7065),semilattice_sup_sup(X7065),hAPP(X7065,X7065,hAPP(X7065,fun(X7065,X7065),semilattice_inf_inf(X7065),X7066),X7067)),X7068) = hAPP(X7065,X7065,hAPP(X7065,fun(X7065,X7065),semilattice_inf_inf(X7065),hAPP(X7065,X7065,hAPP(X7065,fun(X7065,X7065),semilattice_sup_sup(X7065),X7066),X7068)),hAPP(X7065,X7065,hAPP(X7065,fun(X7065,X7065),semilattice_sup_sup(X7065),X7067),X7068)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_876_sup__inf__distrib2])])]) ).

fof(i_0_2049,plain,
    ! [X7069,X7070,X7071,X7072] :
      ( ~ distrib_lattice(X7069)
      | hAPP(X7069,X7069,hAPP(X7069,fun(X7069,X7069),semilattice_inf_inf(X7069),hAPP(X7069,X7069,hAPP(X7069,fun(X7069,X7069),semilattice_sup_sup(X7069),X7070),X7071)),X7072) = hAPP(X7069,X7069,hAPP(X7069,fun(X7069,X7069),semilattice_sup_sup(X7069),hAPP(X7069,X7069,hAPP(X7069,fun(X7069,X7069),semilattice_inf_inf(X7069),X7070),X7072)),hAPP(X7069,X7069,hAPP(X7069,fun(X7069,X7069),semilattice_inf_inf(X7069),X7071),X7072)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_877_inf__sup__distrib2])])]) ).

fof(i_0_2050,plain,
    ! [X5991,X5992,X5993,X5994] :
      ( ~ comm_semiring(X5991)
      | hAPP(X5991,X5991,hAPP(X5991,fun(X5991,X5991),times_times(X5991),hAPP(X5991,X5991,hAPP(X5991,fun(X5991,X5991),plus_plus(X5991),X5992),X5993)),X5994) = hAPP(X5991,X5991,hAPP(X5991,fun(X5991,X5991),plus_plus(X5991),hAPP(X5991,X5991,hAPP(X5991,fun(X5991,X5991),times_times(X5991),X5992),X5994)),hAPP(X5991,X5991,hAPP(X5991,fun(X5991,X5991),times_times(X5991),X5993),X5994)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_616_comm__semiring__class_Odistrib])])]) ).

fof(i_0_2051,plain,
    ! [X5886,X5887,X5888,X5889] :
      ( ~ comm_semiring_1(X5886)
      | hAPP(X5886,X5886,hAPP(X5886,fun(X5886,X5886),times_times(X5886),hAPP(X5886,X5886,hAPP(X5886,fun(X5886,X5886),plus_plus(X5886),X5887),X5888)),X5889) = hAPP(X5886,X5886,hAPP(X5886,fun(X5886,X5886),plus_plus(X5886),hAPP(X5886,X5886,hAPP(X5886,fun(X5886,X5886),times_times(X5886),X5887),X5889)),hAPP(X5886,X5886,hAPP(X5886,fun(X5886,X5886),times_times(X5886),X5888),X5889)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_579_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])])]) ).

fof(i_0_2052,plain,
    ! [X6157,X6158] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6157))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6157),X6158))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6158))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6157),X6158))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6157))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6158))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6157),X6158))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_664_nat__0__less__mult__iff])])]) ).

cnf(i_0_2053,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_1268]) ).

cnf(i_0_2054,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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))
    | hAPP(X1,X2,X3,X5) != ti(X2,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1269]) ).

fof(i_0_2055,plain,
    ! [X3958,X3959,X3960,X3962,X3963,X3964,X3965,X3966,X3969] :
      ( ( ~ hBOOL(hAPP(product_prod(X3958,X3959),bool,X3960,esk6_3(X3958,X3959,X3960)))
        | hBOOL(hAPP(product_prod(X3958,X3959),bool,X3960,hAPP(X3959,product_prod(X3958,X3959),hAPP(X3958,fun(X3959,product_prod(X3958,X3959)),product_Pair(X3958,X3959),X3962),X3963))) )
      & ( ~ hBOOL(hAPP(product_prod(X3964,X3965),bool,X3966,hAPP(X3965,product_prod(X3964,X3965),hAPP(X3964,fun(X3965,product_prod(X3964,X3965)),product_Pair(X3964,X3965),esk7_3(X3964,X3965,X3966)),esk8_3(X3964,X3965,X3966))))
        | hBOOL(hAPP(product_prod(X3964,X3965),bool,X3966,X3969)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_split__paired__All])])])])]) ).

fof(i_0_2056,plain,
    ! [X5559,X5560,X5561] :
      ( ~ hBOOL(hAPP(fun(X5559,bool),bool,hAPP(fun(X5559,X5560),fun(fun(X5559,bool),bool),inj_on(X5559,X5560),X5561),top_top(fun(X5559,bool))))
      | hAPP(fun(X5560,bool),fun(X5559,bool),hAPP(fun(X5560,X5559),fun(fun(X5560,bool),fun(X5559,bool)),image(X5560,X5559),hAPP(fun(X5559,X5560),fun(X5560,X5559),hAPP(fun(X5559,bool),fun(fun(X5559,X5560),fun(X5560,X5559)),hilbert_inv_into(X5559,X5560),top_top(fun(X5559,bool))),X5561)),top_top(fun(X5560,bool))) = top_top(fun(X5559,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_507_inj__imp__surj__inv])]) ).

fof(i_0_2057,plain,
    ! [X6795,X6796,X6797,X6798] :
      ( ~ hBOOL(hAPP(fun(X6795,bool),bool,hAPP(X6795,fun(fun(X6795,bool),bool),member(X6795),X6797),X6798))
      | hBOOL(hAPP(fun(X6795,bool),bool,hAPP(X6795,fun(fun(X6795,bool),bool),member(X6795),X6797),hAPP(fun(X6795,bool),fun(X6795,bool),hAPP(fun(X6795,bool),fun(fun(X6795,bool),fun(X6795,bool)),semilattice_sup_sup(fun(X6795,bool)),X6798),X6796))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_802_UnI1])]) ).

fof(i_0_2058,plain,
    ! [X6684,X6685,X6686,X6687] :
      ( ( ~ hBOOL(hAPP(fun(X6684,bool),bool,hAPP(X6684,fun(fun(X6684,bool),bool),member(X6684),X6686),X6687))
        | hBOOL(hAPP(fun(X6684,bool),bool,hAPP(X6684,fun(fun(X6684,bool),bool),member(X6684),X6686),hAPP(fun(X6684,bool),fun(X6684,bool),hAPP(fun(X6684,bool),fun(fun(X6684,bool),fun(X6684,bool)),semilattice_sup_sup(fun(X6684,bool)),X6685),X6687))) )
      & ( ~ hBOOL(hAPP(fun(X6684,bool),bool,hAPP(X6684,fun(fun(X6684,bool),bool),member(X6684),X6686),X6685))
        | hBOOL(hAPP(fun(X6684,bool),bool,hAPP(X6684,fun(fun(X6684,bool),bool),member(X6684),X6686),hAPP(fun(X6684,bool),fun(X6684,bool),hAPP(fun(X6684,bool),fun(fun(X6684,bool),fun(X6684,bool)),semilattice_sup_sup(fun(X6684,bool)),X6685),X6687))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1270])])]) ).

fof(i_0_2059,plain,
    ! [X6799,X6800,X6801,X6802] :
      ( ~ hBOOL(hAPP(fun(X6799,bool),bool,hAPP(X6799,fun(fun(X6799,bool),bool),member(X6799),X6801),X6802))
      | hBOOL(hAPP(fun(X6799,bool),bool,hAPP(X6799,fun(fun(X6799,bool),bool),member(X6799),X6801),hAPP(fun(X6799,bool),fun(X6799,bool),hAPP(fun(X6799,bool),fun(fun(X6799,bool),fun(X6799,bool)),semilattice_sup_sup(fun(X6799,bool)),X6800),X6802))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_803_UnI2])]) ).

fof(i_0_2060,plain,
    ! [X6755,X6756,X6757,X6758] : hAPP(fun(X6755,bool),fun(X6755,bool),hAPP(fun(X6755,bool),fun(fun(X6755,bool),fun(X6755,bool)),semilattice_sup_sup(fun(X6755,bool)),hAPP(fun(X6755,bool),fun(X6755,bool),hAPP(fun(X6755,bool),fun(fun(X6755,bool),fun(X6755,bool)),semilattice_sup_sup(fun(X6755,bool)),X6756),X6757)),X6758) = hAPP(fun(X6755,bool),fun(X6755,bool),hAPP(fun(X6755,bool),fun(fun(X6755,bool),fun(X6755,bool)),semilattice_sup_sup(fun(X6755,bool)),X6756),hAPP(fun(X6755,bool),fun(X6755,bool),hAPP(fun(X6755,bool),fun(fun(X6755,bool),fun(X6755,bool)),semilattice_sup_sup(fun(X6755,bool)),X6757),X6758)),
    inference(variable_rename,[status(thm)],[fact_797_Un__assoc]) ).

fof(i_0_2061,plain,
    ! [X7171,X7172,X7173,X7174] : hAPP(fun(X7171,bool),fun(X7171,bool),hAPP(fun(X7171,bool),fun(fun(X7171,bool),fun(X7171,bool)),semilattice_inf_inf(fun(X7171,bool)),hAPP(fun(X7171,bool),fun(X7171,bool),hAPP(fun(X7171,bool),fun(fun(X7171,bool),fun(X7171,bool)),semilattice_inf_inf(fun(X7171,bool)),X7172),X7173)),X7174) = hAPP(fun(X7171,bool),fun(X7171,bool),hAPP(fun(X7171,bool),fun(fun(X7171,bool),fun(X7171,bool)),semilattice_inf_inf(fun(X7171,bool)),X7172),hAPP(fun(X7171,bool),fun(X7171,bool),hAPP(fun(X7171,bool),fun(fun(X7171,bool),fun(X7171,bool)),semilattice_inf_inf(fun(X7171,bool)),X7173),X7174)),
    inference(variable_rename,[status(thm)],[fact_902_Int__assoc]) ).

fof(i_0_2062,plain,
    ! [X5964,X5965,X5966] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5964),X5965)),X5966) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5964),X5966)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5965),X5966)),
    inference(variable_rename,[status(thm)],[fact_604_add__mult__distrib]) ).

cnf(i_0_2063,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_1271]) ).

cnf(i_0_2064,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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_1272]) ).

fof(i_0_2065,plain,
    ! [X5718,X5719] :
      ( ~ ring_char_0(X5718)
      | ~ hBOOL(hAPP(fun(X5718,bool),bool,hAPP(X5718,fun(fun(X5718,bool),bool),member(X5718),X5719),ring_1_Ints(X5718)))
      | hAPP(X5718,X5718,hAPP(X5718,fun(X5718,X5718),plus_plus(X5718),hAPP(X5718,X5718,hAPP(X5718,fun(X5718,X5718),plus_plus(X5718),one_one(X5718)),X5719)),X5719) != zero_zero(X5718) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_543_Ints__odd__nonzero])])]) ).

fof(i_0_2066,plain,
    ! [X5068,X5069] :
      ( ( ~ hBOOL(hAPP(X5068,bool,hAPP(X5068,fun(X5068,bool),ord_less_eq(X5068),zero_zero(X5068)),hAPP(X5068,X5068,hAPP(X5068,fun(X5068,X5068),plus_plus(X5068),X5069),X5069)))
        | hBOOL(hAPP(X5068,bool,hAPP(X5068,fun(X5068,bool),ord_less_eq(X5068),zero_zero(X5068)),X5069))
        | ~ linord219039673up_add(X5068) )
      & ( ~ hBOOL(hAPP(X5068,bool,hAPP(X5068,fun(X5068,bool),ord_less_eq(X5068),zero_zero(X5068)),X5069))
        | hBOOL(hAPP(X5068,bool,hAPP(X5068,fun(X5068,bool),ord_less_eq(X5068),zero_zero(X5068)),hAPP(X5068,X5068,hAPP(X5068,fun(X5068,X5068),plus_plus(X5068),X5069),X5069)))
        | ~ linord219039673up_add(X5068) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_346_zero__le__double__add__iff__zero__le__single__add])])])]) ).

fof(i_0_2067,plain,
    ! [X5082,X5083] :
      ( ( ~ hBOOL(hAPP(X5082,bool,hAPP(X5082,fun(X5082,bool),ord_less(X5082),zero_zero(X5082)),hAPP(X5082,X5082,hAPP(X5082,fun(X5082,X5082),plus_plus(X5082),X5083),X5083)))
        | hBOOL(hAPP(X5082,bool,hAPP(X5082,fun(X5082,bool),ord_less(X5082),zero_zero(X5082)),X5083))
        | ~ linord219039673up_add(X5082) )
      & ( ~ hBOOL(hAPP(X5082,bool,hAPP(X5082,fun(X5082,bool),ord_less(X5082),zero_zero(X5082)),X5083))
        | hBOOL(hAPP(X5082,bool,hAPP(X5082,fun(X5082,bool),ord_less(X5082),zero_zero(X5082)),hAPP(X5082,X5082,hAPP(X5082,fun(X5082,X5082),plus_plus(X5082),X5083),X5083)))
        | ~ linord219039673up_add(X5082) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_zero__less__double__add__iff__zero__less__single__add])])])]) ).

fof(i_0_2068,plain,
    ! [X7239,X7240,X7241,X7242] :
      ( ( hBOOL(hAPP(X7239,bool,hAPP(X7239,fun(X7239,bool),ord_less_eq(X7239),X7240),X7241))
        | ~ hBOOL(hAPP(X7239,bool,hAPP(X7239,fun(X7239,bool),ord_less_eq(X7239),X7240),hAPP(X7239,X7239,hAPP(X7239,fun(X7239,X7239),semilattice_inf_inf(X7239),X7241),X7242)))
        | ~ semilattice_inf(X7239) )
      & ( hBOOL(hAPP(X7239,bool,hAPP(X7239,fun(X7239,bool),ord_less_eq(X7239),X7240),X7242))
        | ~ hBOOL(hAPP(X7239,bool,hAPP(X7239,fun(X7239,bool),ord_less_eq(X7239),X7240),hAPP(X7239,X7239,hAPP(X7239,fun(X7239,X7239),semilattice_inf_inf(X7239),X7241),X7242)))
        | ~ semilattice_inf(X7239) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1273])])])]) ).

cnf(i_0_2069,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ti(X1,X5) = ti(X1,X6)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X3) != ti(X1,X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1274]) ).

fof(i_0_2070,plain,
    ! [X6676,X6677,X6678,X6679] :
      ( ~ hBOOL(hAPP(X6676,bool,hAPP(fun(X6676,bool),fun(X6676,bool),hAPP(fun(X6676,bool),fun(fun(X6676,bool),fun(X6676,bool)),semilattice_sup_sup(fun(X6676,bool)),X6677),X6678),X6679))
      | hBOOL(hAPP(X6676,bool,X6677,X6679))
      | hBOOL(hAPP(X6676,bool,X6678,X6679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1275])]) ).

cnf(i_0_2071,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1276]) ).

cnf(i_0_2072,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1276]) ).

fof(i_0_2073,plain,
    ! [X4639,X4640,X4641,X4642,X4643,X4644] :
      ( ~ hBOOL(hAPP(X4639,bool,hAPP(X4640,fun(X4639,bool),X4642,X4643),X4644))
      | ~ hBOOL(hAPP(fun(X4640,fun(X4639,bool)),bool,hAPP(fun(X4640,fun(X4639,bool)),fun(fun(X4640,fun(X4639,bool)),bool),ord_less_eq(fun(X4640,fun(X4639,bool))),X4642),X4641))
      | hBOOL(hAPP(X4639,bool,hAPP(X4640,fun(X4639,bool),X4641,X4643),X4644)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_201_rev__predicate2D])]) ).

fof(i_0_2074,plain,
    ! [X4648,X4649,X4650,X4651,X4652,X4653] :
      ( ~ hBOOL(hAPP(fun(X4648,fun(X4649,bool)),bool,hAPP(fun(X4648,fun(X4649,bool)),fun(fun(X4648,fun(X4649,bool)),bool),ord_less_eq(fun(X4648,fun(X4649,bool))),X4652),X4653))
      | ~ hBOOL(hAPP(X4649,bool,hAPP(X4648,fun(X4649,bool),X4652,X4650),X4651))
      | hBOOL(hAPP(X4649,bool,hAPP(X4648,fun(X4649,bool),X4653,X4650),X4651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_203_predicate2D])]) ).

fof(i_0_2075,plain,
    ! [X4901,X4902,X4903] :
      ( ~ hBOOL(hAPP(fun(X4901,bool),bool,finite_finite_1(X4901),X4903))
      | ~ hBOOL(hAPP(fun(X4901,bool),bool,hAPP(fun(X4901,bool),fun(fun(X4901,bool),bool),ord_less_eq(fun(X4901,bool)),X4902),X4903))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X4901,bool),nat,finite_card(X4901),X4902)),hAPP(fun(X4901,bool),nat,finite_card(X4901),X4903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_card__mono])]) ).

fof(i_0_2076,plain,
    ! [X4895,X4896,X4897] :
      ( ~ hBOOL(hAPP(fun(X4895,bool),bool,finite_finite_1(X4895),X4897))
      | ~ hBOOL(hAPP(fun(X4895,bool),bool,hAPP(fun(X4895,bool),fun(fun(X4895,bool),bool),ord_less(fun(X4895,bool)),X4896),X4897))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X4895,bool),nat,finite_card(X4895),X4896)),hAPP(fun(X4895,bool),nat,finite_card(X4895),X4897))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_psubset__card__mono])]) ).

cnf(i_0_2077,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_1277]) ).

fof(i_0_2078,plain,
    ! [X6733,X6734,X6735] :
      ( ( hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),X6734))
        | ~ hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),hAPP(fun(X6733,bool),fun(X6733,bool),hAPP(fun(X6733,bool),fun(fun(X6733,bool),fun(X6733,bool)),semilattice_sup_sup(fun(X6733,bool)),X6734),X6735))) )
      & ( hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),X6735))
        | ~ hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),hAPP(fun(X6733,bool),fun(X6733,bool),hAPP(fun(X6733,bool),fun(fun(X6733,bool),fun(X6733,bool)),semilattice_sup_sup(fun(X6733,bool)),X6734),X6735))) )
      & ( ~ hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),X6734))
        | ~ hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),X6735))
        | hBOOL(hAPP(fun(X6733,bool),bool,finite_finite_1(X6733),hAPP(fun(X6733,bool),fun(X6733,bool),hAPP(fun(X6733,bool),fun(fun(X6733,bool),fun(X6733,bool)),semilattice_sup_sup(fun(X6733,bool)),X6734),X6735))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_790_finite__Un])])]) ).

fof(i_0_2079,plain,
    ! [X5208,X5209] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5208),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5208),X5209)))),
    inference(variable_rename,[status(thm)],[fact_413_less__add__Suc1]) ).

fof(i_0_2080,plain,
    ! [X5210,X5211] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5210),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5211),X5210)))),
    inference(variable_rename,[status(thm)],[fact_414_less__add__Suc2]) ).

fof(i_0_2081,plain,
    ! [X4654,X4655,X4656,X4657] :
      ( ~ hBOOL(hAPP(fun(X4654,bool),bool,hAPP(fun(X4654,bool),fun(fun(X4654,bool),bool),ord_less_eq(fun(X4654,bool)),X4656),X4657))
      | ~ hBOOL(hAPP(fun(X4654,bool),bool,hAPP(fun(X4654,bool),fun(fun(X4654,bool),bool),ord_less_eq(fun(X4654,bool)),X4657),X4655))
      | hBOOL(hAPP(fun(X4654,bool),bool,hAPP(fun(X4654,bool),fun(fun(X4654,bool),bool),ord_less_eq(fun(X4654,bool)),X4656),X4655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_204_subset__trans])]) ).

fof(i_0_2082,plain,
    ! [X4631,X4632,X4633,X4634] :
      ( ~ hBOOL(hAPP(fun(X4631,bool),bool,hAPP(fun(X4631,bool),fun(fun(X4631,bool),bool),ord_less(fun(X4631,bool)),X4633),X4634))
      | ~ hBOOL(hAPP(fun(X4631,bool),bool,hAPP(fun(X4631,bool),fun(fun(X4631,bool),bool),ord_less_eq(fun(X4631,bool)),X4634),X4632))
      | hBOOL(hAPP(fun(X4631,bool),bool,hAPP(fun(X4631,bool),fun(fun(X4631,bool),bool),ord_less(fun(X4631,bool)),X4633),X4632)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_199_psubset__subset__trans])]) ).

fof(i_0_2083,plain,
    ! [X4635,X4636,X4637,X4638] :
      ( ~ hBOOL(hAPP(fun(X4635,bool),bool,hAPP(fun(X4635,bool),fun(fun(X4635,bool),bool),ord_less_eq(fun(X4635,bool)),X4637),X4638))
      | ~ hBOOL(hAPP(fun(X4635,bool),bool,hAPP(fun(X4635,bool),fun(fun(X4635,bool),bool),ord_less(fun(X4635,bool)),X4638),X4636))
      | hBOOL(hAPP(fun(X4635,bool),bool,hAPP(fun(X4635,bool),fun(fun(X4635,bool),bool),ord_less(fun(X4635,bool)),X4637),X4636)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_200_subset__psubset__trans])]) ).

fof(i_0_2084,plain,
    ! [X4838,X4839,X4840,X4841] :
      ( ~ hBOOL(hAPP(fun(X4838,bool),bool,hAPP(fun(X4838,bool),fun(fun(X4838,bool),bool),ord_less(fun(X4838,bool)),X4840),X4841))
      | ~ hBOOL(hAPP(fun(X4838,bool),bool,hAPP(fun(X4838,bool),fun(fun(X4838,bool),bool),ord_less(fun(X4838,bool)),X4841),X4839))
      | hBOOL(hAPP(fun(X4838,bool),bool,hAPP(fun(X4838,bool),fun(fun(X4838,bool),bool),ord_less(fun(X4838,bool)),X4840),X4839)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_psubset__trans])]) ).

cnf(i_0_2085,plain,
    ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1278]) ).

fof(i_0_2086,plain,
    ! [X7034,X7035,X7036,X7037] :
      ( ( hBOOL(hAPP(X7034,bool,X7035,X7037))
        | ~ hBOOL(hAPP(X7034,bool,hAPP(fun(X7034,bool),fun(X7034,bool),hAPP(fun(X7034,bool),fun(fun(X7034,bool),fun(X7034,bool)),semilattice_inf_inf(fun(X7034,bool)),X7035),X7036),X7037)) )
      & ( hBOOL(hAPP(X7034,bool,X7036,X7037))
        | ~ hBOOL(hAPP(X7034,bool,hAPP(fun(X7034,bool),fun(X7034,bool),hAPP(fun(X7034,bool),fun(fun(X7034,bool),fun(X7034,bool)),semilattice_inf_inf(fun(X7034,bool)),X7035),X7036),X7037)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1279])])]) ).

fof(i_0_2087,plain,
    ! [X7159,X7160,X7161,X7162] :
      ( ~ hBOOL(hAPP(X7159,bool,hAPP(fun(X7159,bool),fun(X7159,bool),hAPP(fun(X7159,bool),fun(fun(X7159,bool),fun(X7159,bool)),semilattice_inf_inf(fun(X7159,bool)),X7160),X7161),X7162))
      | hBOOL(hAPP(X7159,bool,X7160,X7162)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_899_inf1D1])]) ).

fof(i_0_2088,plain,
    ! [X7155,X7156,X7157,X7158] :
      ( ~ hBOOL(hAPP(X7155,bool,hAPP(fun(X7155,bool),fun(X7155,bool),hAPP(fun(X7155,bool),fun(fun(X7155,bool),fun(X7155,bool)),semilattice_inf_inf(fun(X7155,bool)),X7156),X7157),X7158))
      | hBOOL(hAPP(X7155,bool,X7157,X7158)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_898_inf1D2])]) ).

fof(i_0_2089,plain,
    ! [X5185,X5186] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5185)),hAPP(nat,nat,suc,X5186)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5185),X5186)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5185),X5186))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5185)),hAPP(nat,nat,suc,X5186))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_403_Suc__le__mono])]) ).

fof(i_0_2090,plain,
    ! [X5167,X5168] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5167)),hAPP(nat,nat,suc,X5168)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5167),X5168)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5167),X5168))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5167)),hAPP(nat,nat,suc,X5168))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_394_Suc__less__eq])]) ).

fof(i_0_2091,plain,
    ! [X5150,X5151] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5150)),hAPP(nat,nat,suc,X5151)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5150),X5151)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_386_Suc__less__SucD])]) ).

fof(i_0_2092,plain,
    ! [X5356,X5357,X5358,X5359] : hBOOL(hAPP(fun(X5356,bool),bool,hAPP(X5356,fun(fun(X5356,bool),bool),member(X5356),hAPP(X5357,X5356,X5358,X5359)),hAPP(fun(X5357,bool),fun(X5356,bool),hAPP(fun(X5357,X5356),fun(fun(X5357,bool),fun(X5356,bool)),image(X5357,X5356),X5358),top_top(fun(X5357,bool))))),
    inference(variable_rename,[status(thm)],[fact_464_rangeI]) ).

fof(i_0_2093,plain,
    ! [X4467,X4468,X4469,X4470,X4471] :
      ( ~ hBOOL(hAPP(fun(X4467,bool),bool,hAPP(fun(X4467,X4468),fun(fun(X4467,bool),bool),inj_on(X4467,X4468),X4470),X4471))
      | ~ hBOOL(hAPP(fun(X4467,bool),bool,hAPP(fun(X4467,bool),fun(fun(X4467,bool),bool),ord_less_eq(fun(X4467,bool)),X4469),X4471))
      | hBOOL(hAPP(fun(X4467,bool),bool,hAPP(fun(X4467,X4468),fun(fun(X4467,bool),bool),inj_on(X4467,X4468),X4470),X4469)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_subset__inj__on])]) ).

cnf(i_0_2094,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_1280]) ).

cnf(i_0_2095,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_1280]) ).

cnf(i_0_2096,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_1280]) ).

cnf(i_0_2097,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_1281]) ).

cnf(i_0_2098,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_1282]) ).

fof(i_0_2099,plain,
    ! [X5156,X5157,X5158] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5157),X5158))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5158),X5156))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5157)),X5156)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_389_less__trans__Suc])]) ).

fof(i_0_2100,plain,
    ! [X6555,X6556,X6557,X6558,X6559] :
      ( ~ hBOOL(hAPP(fun(fun(X6555,bool),fun(X6556,X6556)),bool,hAPP(fun(X6555,fun(X6556,X6556)),fun(fun(fun(X6555,bool),fun(X6556,X6556)),bool),finite_folding_idem(X6555,X6556),X6558),X6559))
      | hAPP(fun(X6556,X6556),fun(X6556,X6556),hAPP(fun(X6556,X6556),fun(fun(X6556,X6556),fun(X6556,X6556)),comp(X6556,X6556,X6556),hAPP(X6555,fun(X6556,X6556),X6558,X6557)),hAPP(X6555,fun(X6556,X6556),X6558,X6557)) = hAPP(X6555,fun(X6556,X6556),X6558,X6557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_750_folding__idem_Oidem__comp])]) ).

fof(i_0_2101,plain,
    ! [X6981,X6982,X6983] :
      ( ~ linorder(X6981)
      | ~ hBOOL(hAPP(X6981,bool,hAPP(X6981,fun(X6981,bool),ord_less(X6981),X6982),X6983))
      | hAPP(fun(X6981,bool),fun(X6981,bool),hAPP(fun(X6981,bool),fun(fun(X6981,bool),fun(X6981,bool)),semilattice_sup_sup(fun(X6981,bool)),hAPP(X6981,fun(X6981,bool),hAPP(X6981,fun(X6981,fun(X6981,bool)),ord_gr676655987ssThan(X6981),X6982),X6983)),hAPP(X6981,fun(X6981,bool),ord_atLeast(X6981),X6983)) = hAPP(X6981,fun(X6981,bool),ord_greaterThan(X6981),X6982) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_854_ivl__disj__un_I12_J])])]) ).

fof(i_0_2102,plain,
    ! [X6833,X6834,X6835] :
      ( ~ linorder(X6833)
      | ~ hBOOL(hAPP(X6833,bool,hAPP(X6833,fun(X6833,bool),ord_less_eq(X6833),X6834),X6835))
      | hAPP(fun(X6833,bool),fun(X6833,bool),hAPP(fun(X6833,bool),fun(fun(X6833,bool),fun(X6833,bool)),semilattice_sup_sup(fun(X6833,bool)),hAPP(X6833,fun(X6833,bool),hAPP(X6833,fun(X6833,fun(X6833,bool)),ord_gr1471790799AtMost(X6833),X6834),X6835)),hAPP(X6833,fun(X6833,bool),ord_greaterThan(X6833),X6835)) = hAPP(X6833,fun(X6833,bool),ord_greaterThan(X6833),X6834) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_812_ivl__disj__un_I11_J])])]) ).

fof(i_0_2103,plain,
    ! [X7021,X7022,X7023] :
      ( ~ linorder(X7021)
      | ~ hBOOL(hAPP(X7021,bool,hAPP(X7021,fun(X7021,bool),ord_less_eq(X7021),X7022),X7023))
      | hAPP(fun(X7021,bool),fun(X7021,bool),hAPP(fun(X7021,bool),fun(fun(X7021,bool),fun(X7021,bool)),semilattice_sup_sup(fun(X7021,bool)),hAPP(X7021,fun(X7021,bool),hAPP(X7021,fun(X7021,fun(X7021,bool)),ord_atLeastLessThan(X7021),X7022),X7023)),hAPP(X7021,fun(X7021,bool),ord_atLeast(X7021),X7023)) = hAPP(X7021,fun(X7021,bool),ord_atLeast(X7021),X7022) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_865_ivl__disj__un_I14_J])])]) ).

fof(i_0_2104,plain,
    ! [X6984,X6985,X6986] :
      ( ~ linorder(X6984)
      | ~ hBOOL(hAPP(X6984,bool,hAPP(X6984,fun(X6984,bool),ord_less_eq(X6984),X6985),X6986))
      | hAPP(fun(X6984,bool),fun(X6984,bool),hAPP(fun(X6984,bool),fun(fun(X6984,bool),fun(X6984,bool)),semilattice_sup_sup(fun(X6984,bool)),hAPP(X6984,fun(X6984,bool),hAPP(X6984,fun(X6984,fun(X6984,bool)),ord_atLeastAtMost(X6984),X6985),X6986)),hAPP(X6984,fun(X6984,bool),ord_greaterThan(X6984),X6986)) = hAPP(X6984,fun(X6984,bool),ord_atLeast(X6984),X6985) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_855_ivl__disj__un_I13_J])])]) ).

fof(i_0_2105,plain,
    ! [X6471,X6472,X6473,X6474,X6475,X6476,X6477,X6478,X6479,X6480,X6481] :
      ( hAPP(X6471,X6472,X6476,hAPP(X6473,X6471,X6477,X6478)) != hAPP(X6474,X6472,X6479,hAPP(X6475,X6474,X6480,X6481))
      | hAPP(X6473,X6472,hAPP(fun(X6473,X6471),fun(X6473,X6472),hAPP(fun(X6471,X6472),fun(fun(X6473,X6471),fun(X6473,X6472)),comp(X6471,X6472,X6473),X6476),X6477),X6478) = hAPP(X6475,X6472,hAPP(fun(X6475,X6474),fun(X6475,X6472),hAPP(fun(X6474,X6472),fun(fun(X6475,X6474),fun(X6475,X6472)),comp(X6474,X6472,X6475),X6479),X6480),X6481) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_735_comp__cong])]) ).

fof(i_0_2106,plain,
    ! [X6135,X6136,X6137] :
      ( ~ comm_semiring_1(X6135)
      | hAPP(X6135,X6135,hAPP(X6135,fun(X6135,X6135),plus_plus(X6135),hAPP(X6135,X6135,hAPP(X6135,fun(X6135,X6135),times_times(X6135),X6136),X6137)),X6137) = hAPP(X6135,X6135,hAPP(X6135,fun(X6135,X6135),times_times(X6135),hAPP(X6135,X6135,hAPP(X6135,fun(X6135,X6135),plus_plus(X6135),X6136),one_one(X6135))),X6137) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])]) ).

fof(i_0_2107,plain,
    ! [X7073,X7074,X7075,X7076] :
      ( ~ distrib_lattice(X7073)
      | hAPP(X7073,X7073,hAPP(X7073,fun(X7073,X7073),semilattice_sup_sup(X7073),X7074),hAPP(X7073,X7073,hAPP(X7073,fun(X7073,X7073),semilattice_inf_inf(X7073),X7075),X7076)) = hAPP(X7073,X7073,hAPP(X7073,fun(X7073,X7073),semilattice_inf_inf(X7073),hAPP(X7073,X7073,hAPP(X7073,fun(X7073,X7073),semilattice_sup_sup(X7073),X7074),X7075)),hAPP(X7073,X7073,hAPP(X7073,fun(X7073,X7073),semilattice_sup_sup(X7073),X7074),X7076)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_878_sup__inf__distrib1])])]) ).

fof(i_0_2108,plain,
    ! [X7077,X7078,X7079,X7080] :
      ( ~ distrib_lattice(X7077)
      | hAPP(X7077,X7077,hAPP(X7077,fun(X7077,X7077),semilattice_inf_inf(X7077),X7078),hAPP(X7077,X7077,hAPP(X7077,fun(X7077,X7077),semilattice_sup_sup(X7077),X7079),X7080)) = hAPP(X7077,X7077,hAPP(X7077,fun(X7077,X7077),semilattice_sup_sup(X7077),hAPP(X7077,X7077,hAPP(X7077,fun(X7077,X7077),semilattice_inf_inf(X7077),X7078),X7079)),hAPP(X7077,X7077,hAPP(X7077,fun(X7077,X7077),semilattice_inf_inf(X7077),X7078),X7080)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_879_inf__sup__distrib1])])]) ).

fof(i_0_2109,plain,
    ! [X5895,X5896,X5897,X5898] :
      ( ~ comm_semiring_1(X5895)
      | hAPP(X5895,X5895,hAPP(X5895,fun(X5895,X5895),times_times(X5895),X5896),hAPP(X5895,X5895,hAPP(X5895,fun(X5895,X5895),plus_plus(X5895),X5897),X5898)) = hAPP(X5895,X5895,hAPP(X5895,fun(X5895,X5895),plus_plus(X5895),hAPP(X5895,X5895,hAPP(X5895,fun(X5895,X5895),times_times(X5895),X5896),X5897)),hAPP(X5895,X5895,hAPP(X5895,fun(X5895,X5895),times_times(X5895),X5896),X5898)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_581_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])]) ).

fof(i_0_2110,plain,
    ! [X5918,X5919,X5920,X5921] :
      ( ~ comm_semiring_1(X5918)
      | hAPP(X5918,X5918,hAPP(X5918,fun(X5918,X5918),times_times(X5918),hAPP(X5918,X5918,hAPP(X5918,fun(X5918,X5918),times_times(X5918),X5919),X5920)),X5921) = hAPP(X5918,X5918,hAPP(X5918,fun(X5918,X5918),times_times(X5918),hAPP(X5918,X5918,hAPP(X5918,fun(X5918,X5918),times_times(X5918),X5919),X5921)),X5920) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])]) ).

fof(i_0_2111,plain,
    ! [X5304,X5305,X5306,X5307] :
      ( ~ comm_semiring_1(X5304)
      | hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),X5305),X5306)),X5307) = hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),hAPP(X5304,X5304,hAPP(X5304,fun(X5304,X5304),plus_plus(X5304),X5305),X5307)),X5306) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])]) ).

fof(i_0_2112,plain,
    ! [X7286,X7287,X7288] :
      ( ~ lattice(X7286)
      | hBOOL(hAPP(X7286,bool,hAPP(X7286,fun(X7286,bool),ord_less_eq(X7286),hAPP(X7286,X7286,hAPP(X7286,fun(X7286,X7286),semilattice_inf_inf(X7286),X7287),X7288)),X7287)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_933_inf__sup__ord_I1_J])])]) ).

fof(i_0_2113,plain,
    ! [X7283,X7284,X7285] :
      ( ~ semilattice_inf(X7283)
      | hBOOL(hAPP(X7283,bool,hAPP(X7283,fun(X7283,bool),ord_less_eq(X7283),hAPP(X7283,X7283,hAPP(X7283,fun(X7283,X7283),semilattice_inf_inf(X7283),X7284),X7285)),X7284)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_932_inf__le1])])]) ).

fof(i_0_2114,plain,
    ! [X7280,X7281,X7282] :
      ( ~ lattice(X7280)
      | hBOOL(hAPP(X7280,bool,hAPP(X7280,fun(X7280,bool),ord_less_eq(X7280),hAPP(X7280,X7280,hAPP(X7280,fun(X7280,X7280),semilattice_inf_inf(X7280),X7281),X7282)),X7282)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_931_inf__sup__ord_I2_J])])]) ).

fof(i_0_2115,plain,
    ! [X7277,X7278,X7279] :
      ( ~ semilattice_inf(X7277)
      | hBOOL(hAPP(X7277,bool,hAPP(X7277,fun(X7277,bool),ord_less_eq(X7277),hAPP(X7277,X7277,hAPP(X7277,fun(X7277,X7277),semilattice_inf_inf(X7277),X7278),X7279)),X7279)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_930_inf__le2])])]) ).

fof(i_0_2116,plain,
    ! [X4979,X4980,X4981,X4982] :
      ( ~ hBOOL(hAPP(fun(X4980,bool),bool,finite_finite_1(X4980),X4982))
      | ~ hBOOL(hAPP(fun(X4979,bool),bool,finite_finite_1(X4979),X4981))
      | hBOOL(hAPP(fun(sum_sum(X4980,X4979),bool),bool,finite_finite_1(sum_sum(X4980,X4979)),hAPP(fun(X4979,bool),fun(sum_sum(X4980,X4979),bool),hAPP(fun(X4980,bool),fun(fun(X4979,bool),fun(sum_sum(X4980,X4979),bool)),sum_Plus(X4980,X4979),X4982),X4981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_finite__Plus])]) ).

cnf(i_0_2117,plain,
    ( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = ti(fun(X1,X2),X3)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1283]) ).

fof(i_0_2118,plain,
    ! [X4662,X4663,X4664,X4665] :
      ( ~ hBOOL(hAPP(fun(X4662,bool),bool,hAPP(X4662,fun(fun(X4662,bool),bool),member(X4662),X4664),X4665))
      | ~ hBOOL(hAPP(fun(X4662,bool),bool,hAPP(fun(X4662,bool),fun(fun(X4662,bool),bool),ord_less_eq(fun(X4662,bool)),X4665),X4663))
      | hBOOL(hAPP(fun(X4662,bool),bool,hAPP(X4662,fun(fun(X4662,bool),bool),member(X4662),X4664),X4663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_206_set__rev__mp])]) ).

fof(i_0_2119,plain,
    ! [X4670,X4671,X4672,X4673] :
      ( ~ hBOOL(hAPP(fun(X4670,bool),bool,hAPP(fun(X4670,bool),fun(fun(X4670,bool),bool),ord_less_eq(fun(X4670,bool)),X4672),X4673))
      | ~ hBOOL(hAPP(fun(X4670,bool),bool,hAPP(X4670,fun(fun(X4670,bool),bool),member(X4670),X4671),X4672))
      | hBOOL(hAPP(fun(X4670,bool),bool,hAPP(X4670,fun(fun(X4670,bool),bool),member(X4670),X4671),X4673)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_208_in__mono])]) ).

fof(i_0_2120,plain,
    ! [X4658,X4659,X4660,X4661] :
      ( ~ hBOOL(hAPP(fun(X4658,bool),bool,hAPP(fun(X4658,bool),fun(fun(X4658,bool),bool),ord_less_eq(fun(X4658,bool)),X4660),X4661))
      | ~ hBOOL(hAPP(fun(X4658,bool),bool,hAPP(X4658,fun(fun(X4658,bool),bool),member(X4658),X4659),X4660))
      | hBOOL(hAPP(fun(X4658,bool),bool,hAPP(X4658,fun(fun(X4658,bool),bool),member(X4658),X4659),X4661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_205_set__mp])]) ).

fof(i_0_2121,plain,
    ! [X4618,X4619,X4620,X4621] :
      ( ~ hBOOL(hAPP(fun(X4618,bool),bool,hAPP(fun(X4618,bool),fun(fun(X4618,bool),bool),ord_less_eq(fun(X4618,bool)),X4620),X4621))
      | ~ hBOOL(hAPP(fun(X4618,bool),bool,hAPP(X4618,fun(fun(X4618,bool),bool),member(X4618),X4619),X4620))
      | hBOOL(hAPP(fun(X4618,bool),bool,hAPP(X4618,fun(fun(X4618,bool),bool),member(X4618),X4619),X4621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_195_subsetD])]) ).

fof(i_0_2122,plain,
    ! [X4834,X4835,X4836,X4837] :
      ( ~ hBOOL(hAPP(fun(X4834,bool),bool,hAPP(fun(X4834,bool),fun(fun(X4834,bool),bool),ord_less(fun(X4834,bool)),X4836),X4837))
      | ~ hBOOL(hAPP(fun(X4834,bool),bool,hAPP(X4834,fun(fun(X4834,bool),bool),member(X4834),X4835),X4836))
      | hBOOL(hAPP(fun(X4834,bool),bool,hAPP(X4834,fun(fun(X4834,bool),bool),member(X4834),X4835),X4837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_psubsetD])]) ).

fof(i_0_2123,plain,
    ! [X4234,X4235,X4236,X4237,X4238] :
      ( ~ ord(X4235)
      | ~ hBOOL(hAPP(fun(X4234,X4235),bool,hAPP(fun(X4234,X4235),fun(fun(X4234,X4235),bool),ord_less_eq(fun(X4234,X4235)),X4237),X4238))
      | hBOOL(hAPP(X4235,bool,hAPP(X4235,fun(X4235,bool),ord_less_eq(X4235),hAPP(X4234,X4235,X4237,X4236)),hAPP(X4234,X4235,X4238,X4236))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_106_le__funD])])]) ).

fof(i_0_2124,plain,
    ! [X4196,X4197,X4198,X4199,X4200] :
      ( ~ ord(X4197)
      | ~ hBOOL(hAPP(fun(X4196,X4197),bool,hAPP(fun(X4196,X4197),fun(fun(X4196,X4197),bool),ord_less_eq(fun(X4196,X4197)),X4199),X4200))
      | hBOOL(hAPP(X4197,bool,hAPP(X4197,fun(X4197,bool),ord_less_eq(X4197),hAPP(X4196,X4197,X4199,X4198)),hAPP(X4196,X4197,X4200,X4198))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_le__funE])])]) ).

fof(i_0_2125,plain,
    ! [X5189,X5190] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5189),X5190))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5190)),X5189)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5190)),X5189))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5189),X5190)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1284])]) ).

cnf(i_0_2126,plain,
    ( hAPP(X1,X2,X3,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),X4)) = ti(X2,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_1257]) ).

cnf(i_0_2127,plain,
    ( hAPP(X1,X2,X3,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),X4)) = ti(X2,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_1285]) ).

fof(i_0_2128,plain,
    ! [X7378,X7379,X7380] :
      ( ~ comm_monoid_add(X7378)
      | hAPP(nat,X7378,X7380,zero_zero(nat)) != zero_zero(X7378)
      | hAPP(fun(nat,bool),X7378,hAPP(fun(nat,X7378),fun(fun(nat,bool),X7378),big_co1399186613setsum(nat,X7378),X7380),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X7379)) = hAPP(fun(nat,bool),X7378,hAPP(fun(nat,X7378),fun(fun(nat,bool),X7378),big_co1399186613setsum(nat,X7378),X7380),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X7379)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_959_setsum__shift__lb__Suc0__0__upt])])]) ).

cnf(i_0_2129,plain,
    ( ti(fun(X1,bool),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1286]) ).

cnf(i_0_2130,plain,
    ( ti(fun(X1,bool),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk119_2(X1,X2)),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)),esk118_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1254]) ).

fof(i_0_2131,plain,
    ! [X7365,X7366] :
      ( hAPP(nat,nat,X7366,zero_zero(nat)) != zero_zero(nat)
      | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X7366),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X7365)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X7366),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X7365)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_956_setsum__shift__lb__Suc0__0])]) ).

cnf(i_0_2132,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_1287]) ).

fof(i_0_2133,plain,
    ! [X5967,X5968,X5969] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5967),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5968),X5969)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5967),X5968)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5967),X5969)),
    inference(variable_rename,[status(thm)],[fact_605_add__mult__distrib2]) ).

fof(i_0_2134,plain,
    ! [X4452,X4453,X4454,X4455] :
      ( ( hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less_eq(fun(X4452,X4453)),X4454),X4455))
        | ~ hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less(fun(X4452,X4453)),X4454),X4455))
        | ~ ord(X4453) )
      & ( ~ hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less_eq(fun(X4452,X4453)),X4455),X4454))
        | ~ hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less(fun(X4452,X4453)),X4454),X4455))
        | ~ ord(X4453) )
      & ( ~ hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less_eq(fun(X4452,X4453)),X4454),X4455))
        | hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less_eq(fun(X4452,X4453)),X4455),X4454))
        | hBOOL(hAPP(fun(X4452,X4453),bool,hAPP(fun(X4452,X4453),fun(fun(X4452,X4453),bool),ord_less(fun(X4452,X4453)),X4454),X4455))
        | ~ ord(X4453) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1288])])])]) ).

cnf(i_0_2135,plain,
    ( ti(fun(X1,bool),X4) = ti(fun(X1,bool),X5)
    | 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),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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_1289]) ).

cnf(i_0_2136,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)
    | 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))
    | hAPP(X2,X1,X4,hAPP(X1,X2,X3,esk110_4(X1,X2,X4,X3))) != ti(X1,esk110_4(X1,X2,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1290]) ).

fof(i_0_2137,plain,
    ! [X6938,X6939,X6940,X6941] :
      ( ~ semilattice_sup(X6938)
      | ~ hBOOL(hAPP(X6938,bool,hAPP(X6938,fun(X6938,bool),ord_less_eq(X6938),X6940),X6941))
      | hBOOL(hAPP(X6938,bool,hAPP(X6938,fun(X6938,bool),ord_less_eq(X6938),X6940),hAPP(X6938,X6938,hAPP(X6938,fun(X6938,X6938),semilattice_sup_sup(X6938),X6941),X6939))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_842_le__supI1])])]) ).

fof(i_0_2138,plain,
    ! [X6942,X6943,X6944,X6945] :
      ( ~ semilattice_sup(X6942)
      | ~ hBOOL(hAPP(X6942,bool,hAPP(X6942,fun(X6942,bool),ord_less_eq(X6942),X6944),X6945))
      | hBOOL(hAPP(X6942,bool,hAPP(X6942,fun(X6942,bool),ord_less_eq(X6942),X6944),hAPP(X6942,X6942,hAPP(X6942,fun(X6942,X6942),semilattice_sup_sup(X6942),X6943),X6945))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_843_le__supI2])])]) ).

fof(i_0_2139,plain,
    ! [X6973,X6974,X6975,X6976] :
      ( ~ semilattice_sup(X6973)
      | ~ hBOOL(hAPP(X6973,bool,hAPP(X6973,fun(X6973,bool),ord_less(X6973),X6975),X6976))
      | hBOOL(hAPP(X6973,bool,hAPP(X6973,fun(X6973,bool),ord_less(X6973),X6975),hAPP(X6973,X6973,hAPP(X6973,fun(X6973,X6973),semilattice_sup_sup(X6973),X6976),X6974))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_851_less__supI1])])]) ).

fof(i_0_2140,plain,
    ! [X6969,X6970,X6971,X6972] :
      ( ~ semilattice_sup(X6969)
      | ~ hBOOL(hAPP(X6969,bool,hAPP(X6969,fun(X6969,bool),ord_less(X6969),X6971),X6972))
      | hBOOL(hAPP(X6969,bool,hAPP(X6969,fun(X6969,bool),ord_less(X6969),X6971),hAPP(X6969,X6969,hAPP(X6969,fun(X6969,X6969),semilattice_sup_sup(X6969),X6970),X6972))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_850_less__supI2])])]) ).

cnf(i_0_2141,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X4) = hAPP(nat,nat,suc,zero_zero(nat))
    | ti(X1,X2) != ti(X1,esk176_4(X1,X3,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,nat,X3,X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]) ).

cnf(i_0_2142,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_1292]) ).

fof(i_0_2143,plain,
    ! [X5003,X5004,X5005,X5006] :
      ( ( ~ hBOOL(hAPP(fun(X5004,bool),bool,finite_finite_1(X5004),X5006))
        | ~ hBOOL(hAPP(fun(X5003,bool),bool,finite_finite_1(X5003),X5005))
        | hAPP(fun(sum_sum(X5004,X5003),bool),nat,finite_card(sum_sum(X5004,X5003)),hAPP(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool),hAPP(fun(X5004,bool),fun(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool)),sum_Plus(X5004,X5003),X5006),X5005)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X5004,bool),nat,finite_card(X5004),X5006)),hAPP(fun(X5003,bool),nat,finite_card(X5003),X5005)) )
      & ( hBOOL(hAPP(fun(X5004,bool),bool,finite_finite_1(X5004),X5006))
        | hAPP(fun(sum_sum(X5004,X5003),bool),nat,finite_card(sum_sum(X5004,X5003)),hAPP(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool),hAPP(fun(X5004,bool),fun(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool)),sum_Plus(X5004,X5003),X5006),X5005)) = zero_zero(nat) )
      & ( hBOOL(hAPP(fun(X5003,bool),bool,finite_finite_1(X5003),X5005))
        | hAPP(fun(sum_sum(X5004,X5003),bool),nat,finite_card(sum_sum(X5004,X5003)),hAPP(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool),hAPP(fun(X5004,bool),fun(fun(X5003,bool),fun(sum_sum(X5004,X5003),bool)),sum_Plus(X5004,X5003),X5006),X5005)) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_316_card__Plus__conv__if])])]) ).

fof(i_0_2144,plain,
    ! [X4952,X4953,X4954,X4955] :
      ( ~ hBOOL(hAPP(fun(X4953,bool),bool,finite_finite_1(X4953),X4955))
      | ~ hBOOL(hAPP(fun(X4952,bool),bool,finite_finite_1(X4952),X4954))
      | hAPP(fun(sum_sum(X4953,X4952),bool),nat,finite_card(sum_sum(X4953,X4952)),hAPP(fun(X4952,bool),fun(sum_sum(X4953,X4952),bool),hAPP(fun(X4953,bool),fun(fun(X4952,bool),fun(sum_sum(X4953,X4952),bool)),sum_Plus(X4953,X4952),X4955),X4954)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X4953,bool),nat,finite_card(X4953),X4955)),hAPP(fun(X4952,bool),nat,finite_card(X4952),X4954)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_305_card__Plus])]) ).

cnf(i_0_2145,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_1293]) ).

cnf(i_0_2146,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_1294]) ).

fof(i_0_2147,plain,
    ! [X5526,X5527,X5528,X5529] :
      ( ~ hBOOL(hAPP(fun(X5527,bool),bool,finite_finite_1(X5527),X5529))
      | hAPP(fun(X5526,bool),nat,finite_card(X5526),hAPP(fun(X5527,bool),fun(X5526,bool),hAPP(fun(X5527,X5526),fun(fun(X5527,bool),fun(X5526,bool)),image(X5527,X5526),X5528),X5529)) != hAPP(fun(X5527,bool),nat,finite_card(X5527),X5529)
      | hBOOL(hAPP(fun(X5527,bool),bool,hAPP(fun(X5527,X5526),fun(fun(X5527,bool),bool),inj_on(X5527,X5526),X5528),X5529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_499_eq__card__imp__inj__on])]) ).

fof(i_0_2148,plain,
    ! [X5530,X5531,X5532,X5533] :
      ( ( ~ hBOOL(hAPP(fun(X5531,bool),bool,hAPP(fun(X5531,X5530),fun(fun(X5531,bool),bool),inj_on(X5531,X5530),X5532),X5533))
        | hAPP(fun(X5530,bool),nat,finite_card(X5530),hAPP(fun(X5531,bool),fun(X5530,bool),hAPP(fun(X5531,X5530),fun(fun(X5531,bool),fun(X5530,bool)),image(X5531,X5530),X5532),X5533)) = hAPP(fun(X5531,bool),nat,finite_card(X5531),X5533)
        | ~ hBOOL(hAPP(fun(X5531,bool),bool,finite_finite_1(X5531),X5533)) )
      & ( hAPP(fun(X5530,bool),nat,finite_card(X5530),hAPP(fun(X5531,bool),fun(X5530,bool),hAPP(fun(X5531,X5530),fun(fun(X5531,bool),fun(X5530,bool)),image(X5531,X5530),X5532),X5533)) != hAPP(fun(X5531,bool),nat,finite_card(X5531),X5533)
        | hBOOL(hAPP(fun(X5531,bool),bool,hAPP(fun(X5531,X5530),fun(fun(X5531,bool),bool),inj_on(X5531,X5530),X5532),X5533))
        | ~ hBOOL(hAPP(fun(X5531,bool),bool,finite_finite_1(X5531),X5533)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_500_inj__on__iff__eq__card])])]) ).

fof(i_0_2149,plain,
    ! [X4826,X4827,X4828] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4827),X4828))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4827),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4828),X4826))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_termination__basic__simps_I3_J])]) ).

fof(i_0_2150,plain,
    ! [X4781,X4782,X4783] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4782),X4783))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4782),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4783),X4781))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_trans__le__add1])]) ).

fof(i_0_2151,plain,
    ! [X4829,X4830,X4831] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4830),X4831))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4830),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4829),X4831))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_termination__basic__simps_I4_J])]) ).

fof(i_0_2152,plain,
    ! [X4784,X4785,X4786] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4785),X4786))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4785),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4784),X4786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_trans__le__add2])]) ).

fof(i_0_2153,plain,
    ! [X4845,X4846,X4847] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4846),X4847))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4846),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4847),X4845))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_termination__basic__simps_I1_J])]) ).

fof(i_0_2154,plain,
    ! [X4738,X4739,X4740] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4739),X4740))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4739),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4740),X4738))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236_trans__less__add1])]) ).

fof(i_0_2155,plain,
    ! [X4842,X4843,X4844] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4843),X4844))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4843),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4842),X4844))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_termination__basic__simps_I2_J])]) ).

fof(i_0_2156,plain,
    ! [X4741,X4742,X4743] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4742),X4743))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4742),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4741),X4743))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_237_trans__less__add2])]) ).

cnf(i_0_2157,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_1295]) ).

fof(i_0_2158,plain,
    ! [X5274,X5275] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5274),esk95_2(X5274,X5275)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5274)),X5275)) )
      & ( X5275 = hAPP(nat,nat,suc,esk95_2(X5274,X5275))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5274)),X5275)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_Suc__lessE])])])]) ).

fof(i_0_2159,plain,
    ! [X5179,X5180] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5179)),X5180))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5179),X5180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_400_Suc__leD])]) ).

fof(i_0_2160,plain,
    ! [X5230,X5231] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5230)),X5231))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5230),X5231)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_422_Suc__le__lessD])]) ).

fof(i_0_2161,plain,
    ! [X5222,X5223] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5222)),X5223))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5222),X5223)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5222),X5223))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5222)),X5223)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_418_Suc__le__eq])]) ).

fof(i_0_2162,plain,
    ! [X5218,X5219] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5218),X5219))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5218)),X5219)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5218)),X5219))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5218),X5219)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_416_less__eq__Suc__le])]) ).

fof(i_0_2163,plain,
    ! [X5152,X5153] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5152)),X5153))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5152),X5153)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_387_Suc__lessD])]) ).

fof(i_0_2164,plain,
    ! [X6747,X6748,X6749,X6750] : hAPP(fun(X6747,bool),fun(X6747,bool),hAPP(fun(X6747,bool),fun(fun(X6747,bool),fun(X6747,bool)),semilattice_sup_sup(fun(X6747,bool)),X6748),hAPP(fun(X6747,bool),fun(X6747,bool),hAPP(fun(X6747,bool),fun(fun(X6747,bool),fun(X6747,bool)),semilattice_sup_sup(fun(X6747,bool)),X6749),X6750)) = hAPP(fun(X6747,bool),fun(X6747,bool),hAPP(fun(X6747,bool),fun(fun(X6747,bool),fun(X6747,bool)),semilattice_sup_sup(fun(X6747,bool)),X6749),hAPP(fun(X6747,bool),fun(X6747,bool),hAPP(fun(X6747,bool),fun(fun(X6747,bool),fun(X6747,bool)),semilattice_sup_sup(fun(X6747,bool)),X6748),X6750)),
    inference(variable_rename,[status(thm)],[fact_795_Un__left__commute]) ).

fof(i_0_2165,plain,
    ! [X7179,X7180,X7181,X7182] : hAPP(fun(X7179,bool),fun(X7179,bool),hAPP(fun(X7179,bool),fun(fun(X7179,bool),fun(X7179,bool)),semilattice_inf_inf(fun(X7179,bool)),X7180),hAPP(fun(X7179,bool),fun(X7179,bool),hAPP(fun(X7179,bool),fun(fun(X7179,bool),fun(X7179,bool)),semilattice_inf_inf(fun(X7179,bool)),X7181),X7182)) = hAPP(fun(X7179,bool),fun(X7179,bool),hAPP(fun(X7179,bool),fun(fun(X7179,bool),fun(X7179,bool)),semilattice_inf_inf(fun(X7179,bool)),X7181),hAPP(fun(X7179,bool),fun(X7179,bool),hAPP(fun(X7179,bool),fun(fun(X7179,bool),fun(X7179,bool)),semilattice_inf_inf(fun(X7179,bool)),X7180),X7182)),
    inference(variable_rename,[status(thm)],[fact_904_Int__left__commute]) ).

fof(i_0_2166,plain,
    ! [X6730,X6731,X6732] :
      ( ~ hBOOL(hAPP(fun(X6730,bool),bool,finite_finite_1(X6730),X6732))
      | ~ hBOOL(hAPP(fun(X6730,bool),bool,finite_finite_1(X6730),X6731))
      | hBOOL(hAPP(fun(X6730,bool),bool,finite_finite_1(X6730),hAPP(fun(X6730,bool),fun(X6730,bool),hAPP(fun(X6730,bool),fun(fun(X6730,bool),fun(X6730,bool)),semilattice_sup_sup(fun(X6730,bool)),X6732),X6731))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_finite__UnI])]) ).

fof(i_0_2167,plain,
    ! [X5135,X5136] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5135),X5136))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5135)),hAPP(nat,nat,suc,X5136))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_374_Suc__mono])]) ).

fof(i_0_2168,plain,
    ! [X6347,X6348,X6349,X6350,X6352] :
      ( ( hBOOL(hAPP(X6347,bool,X6349,esk146_3(X6347,X6348,X6349)))
        | ~ hBOOL(hAPP(X6347,bool,X6349,X6350)) )
      & ( ~ hBOOL(hAPP(X6347,bool,X6349,X6352))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X6347,nat,X6348,esk146_3(X6347,X6348,X6349))),hAPP(X6347,nat,X6348,X6352)))
        | ~ hBOOL(hAPP(X6347,bool,X6349,X6350)) ) ),
    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_712_ex__has__least__nat])])])])])]) ).

cnf(i_0_2169,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_1296]) ).

cnf(i_0_2170,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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_1297]) ).

fof(i_0_2171,plain,
    ! [X5745,X5746,X5747,X5748] : hAPP(fun(X5745,bool),fun(X5746,bool),hAPP(fun(X5745,X5746),fun(fun(X5745,bool),fun(X5746,bool)),image(X5745,X5746),hAPP(fun(X5745,bool),fun(X5745,X5746),hAPP(fun(X5745,X5746),fun(fun(X5745,bool),fun(X5745,X5746)),restrict(X5745,X5746),X5747),X5748)),X5748) = hAPP(fun(X5745,bool),fun(X5746,bool),hAPP(fun(X5745,X5746),fun(fun(X5745,bool),fun(X5746,bool)),image(X5745,X5746),X5747),X5748),
    inference(variable_rename,[status(thm)],[fact_550_image__restrict__eq]) ).

fof(i_0_2172,plain,
    ! [X6365,X6366,X6367] :
      ( ( hBOOL(hAPP(X6365,bool,X6367,esk150_3(X6365,X6366,X6367)))
        | hBOOL(hAPP(fun(X6365,bool),bool,hAPP(fun(X6365,bool),fun(fun(X6365,bool),bool),ord_less_eq(fun(X6365,bool)),hAPP(fun(X6365,bool),fun(X6365,bool),collect(X6365),X6367)),hAPP(fun(X6365,bool),fun(X6365,bool),collect(X6365),X6366))) )
      & ( ~ hBOOL(hAPP(X6365,bool,X6366,esk150_3(X6365,X6366,X6367)))
        | hBOOL(hAPP(fun(X6365,bool),bool,hAPP(fun(X6365,bool),fun(fun(X6365,bool),bool),ord_less_eq(fun(X6365,bool)),hAPP(fun(X6365,bool),fun(X6365,bool),collect(X6365),X6367)),hAPP(fun(X6365,bool),fun(X6365,bool),collect(X6365),X6366))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_716_Collect__mono])])])]) ).

fof(i_0_2173,plain,
    ! [X6706,X6707,X6708] : hBOOL(hAPP(fun(X6706,bool),bool,hAPP(fun(X6706,bool),fun(fun(X6706,bool),bool),ord_less_eq(fun(X6706,bool)),X6707),hAPP(fun(X6706,bool),fun(X6706,bool),hAPP(fun(X6706,bool),fun(fun(X6706,bool),fun(X6706,bool)),semilattice_sup_sup(fun(X6706,bool)),X6707),X6708))),
    inference(variable_rename,[status(thm)],[fact_782_Un__upper1]) ).

fof(i_0_2174,plain,
    ! [X6709,X6710,X6711] : hBOOL(hAPP(fun(X6709,bool),bool,hAPP(fun(X6709,bool),fun(fun(X6709,bool),bool),ord_less_eq(fun(X6709,bool)),X6710),hAPP(fun(X6709,bool),fun(X6709,bool),hAPP(fun(X6709,bool),fun(fun(X6709,bool),fun(X6709,bool)),semilattice_sup_sup(fun(X6709,bool)),X6711),X6710))),
    inference(variable_rename,[status(thm)],[fact_783_Un__upper2]) ).

fof(i_0_2175,plain,
    ! [X7046,X7047,X7048,X7049] :
      ( ~ hBOOL(hAPP(X7046,bool,X7048,X7049))
      | ~ hBOOL(hAPP(X7046,bool,X7047,X7049))
      | hBOOL(hAPP(X7046,bool,hAPP(fun(X7046,bool),fun(X7046,bool),hAPP(fun(X7046,bool),fun(fun(X7046,bool),fun(X7046,bool)),semilattice_inf_inf(fun(X7046,bool)),X7048),X7047),X7049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_871_inf1I])]) ).

cnf(i_0_2176,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_1298]) ).

cnf(i_0_2177,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X4) = one_one(nat)
    | ti(X1,X2) != ti(X1,esk178_4(X1,X3,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,nat,X3,X2) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]) ).

cnf(i_0_2178,plain,
    ( 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)
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),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_1289]) ).

cnf(i_0_2179,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_1298]) ).

cnf(i_0_2180,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_1298]) ).

fof(i_0_2181,plain,
    ! [X4208,X4209,X4210,X4211] :
      ( ~ preorder(X4208)
      | ~ hBOOL(hAPP(X4208,bool,hAPP(X4208,fun(X4208,bool),ord_less_eq(X4208),X4210),X4211))
      | ~ hBOOL(hAPP(X4208,bool,hAPP(X4208,fun(X4208,bool),ord_less_eq(X4208),X4211),X4209))
      | hBOOL(hAPP(X4208,bool,hAPP(X4208,fun(X4208,bool),ord_less_eq(X4208),X4210),X4209)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_order__trans])])]) ).

fof(i_0_2182,plain,
    ! [X4201,X4202,X4203,X4204] :
      ( ~ order(X4201)
      | ~ hBOOL(hAPP(X4201,bool,hAPP(X4201,fun(X4201,bool),ord_less_eq(X4201),X4203),X4204))
      | ~ hBOOL(hAPP(X4201,bool,hAPP(X4201,fun(X4201,bool),ord_less_eq(X4201),X4202),X4203))
      | hBOOL(hAPP(X4201,bool,hAPP(X4201,fun(X4201,bool),ord_less_eq(X4201),X4202),X4204)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_xt1_I6_J])])]) ).

fof(i_0_2183,plain,
    ! [X4307,X4308,X4309,X4310] :
      ( ~ preorder(X4307)
      | ~ hBOOL(hAPP(X4307,bool,hAPP(X4307,fun(X4307,bool),ord_less(X4307),X4309),X4310))
      | ~ hBOOL(hAPP(X4307,bool,hAPP(X4307,fun(X4307,bool),ord_less_eq(X4307),X4310),X4308))
      | hBOOL(hAPP(X4307,bool,hAPP(X4307,fun(X4307,bool),ord_less(X4307),X4309),X4308)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_128_order__less__le__trans])])]) ).

fof(i_0_2184,plain,
    ! [X4315,X4316,X4317,X4318] :
      ( ~ preorder(X4315)
      | ~ hBOOL(hAPP(X4315,bool,hAPP(X4315,fun(X4315,bool),ord_less_eq(X4315),X4317),X4318))
      | ~ hBOOL(hAPP(X4315,bool,hAPP(X4315,fun(X4315,bool),ord_less(X4315),X4318),X4316))
      | hBOOL(hAPP(X4315,bool,hAPP(X4315,fun(X4315,bool),ord_less(X4315),X4317),X4316)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_130_order__le__less__trans])])]) ).

fof(i_0_2185,plain,
    ! [X4059,X4060,X4061,X4062] :
      ( ~ preorder(X4059)
      | ~ hBOOL(hAPP(X4059,bool,hAPP(X4059,fun(X4059,bool),ord_less(X4059),X4061),X4062))
      | ~ hBOOL(hAPP(X4059,bool,hAPP(X4059,fun(X4059,bool),ord_less(X4059),X4062),X4060))
      | hBOOL(hAPP(X4059,bool,hAPP(X4059,fun(X4059,bool),ord_less(X4059),X4061),X4060)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_order__less__trans])])]) ).

fof(i_0_2186,plain,
    ! [X4311,X4312,X4313,X4314] :
      ( ~ order(X4311)
      | ~ hBOOL(hAPP(X4311,bool,hAPP(X4311,fun(X4311,bool),ord_less(X4311),X4313),X4314))
      | ~ hBOOL(hAPP(X4311,bool,hAPP(X4311,fun(X4311,bool),ord_less_eq(X4311),X4312),X4313))
      | hBOOL(hAPP(X4311,bool,hAPP(X4311,fun(X4311,bool),ord_less(X4311),X4312),X4314)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_129_xt1_I7_J])])]) ).

fof(i_0_2187,plain,
    ! [X4319,X4320,X4321,X4322] :
      ( ~ order(X4319)
      | ~ hBOOL(hAPP(X4319,bool,hAPP(X4319,fun(X4319,bool),ord_less_eq(X4319),X4321),X4322))
      | ~ hBOOL(hAPP(X4319,bool,hAPP(X4319,fun(X4319,bool),ord_less(X4319),X4320),X4321))
      | hBOOL(hAPP(X4319,bool,hAPP(X4319,fun(X4319,bool),ord_less(X4319),X4320),X4322)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_131_xt1_I8_J])])]) ).

fof(i_0_2188,plain,
    ! [X4055,X4056,X4057,X4058] :
      ( ~ order(X4055)
      | ~ hBOOL(hAPP(X4055,bool,hAPP(X4055,fun(X4055,bool),ord_less(X4055),X4057),X4058))
      | ~ hBOOL(hAPP(X4055,bool,hAPP(X4055,fun(X4055,bool),ord_less(X4055),X4056),X4057))
      | hBOOL(hAPP(X4055,bool,hAPP(X4055,fun(X4055,bool),ord_less(X4055),X4056),X4058)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_xt1_I10_J])])]) ).

cnf(i_0_2189,plain,
    ( ti(X1,esk175_3(X1,X4,X3)) = ti(X1,X2)
    | hAPP(X1,nat,X4,X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X4),X3) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]) ).

fof(i_0_2190,plain,
    ! [X4724,X4725,X4726] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4725),X4726))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4726),X4724))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4725),X4724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_230_le__trans])]) ).

fof(i_0_2191,plain,
    ! [X4751,X4752,X4753,X4754] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4753),X4754))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4751),X4754) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4753),X4752)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4751),X4752)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_less__add__eq__less])]) ).

fof(i_0_2192,plain,
    ! [X6138,X6139,X6140] :
      ( ~ comm_semiring_1(X6138)
      | hAPP(X6138,X6138,hAPP(X6138,fun(X6138,X6138),plus_plus(X6138),X6139),hAPP(X6138,X6138,hAPP(X6138,fun(X6138,X6138),times_times(X6138),X6140),X6139)) = hAPP(X6138,X6138,hAPP(X6138,fun(X6138,X6138),times_times(X6138),hAPP(X6138,X6138,hAPP(X6138,fun(X6138,X6138),plus_plus(X6138),X6140),one_one(X6138))),X6139) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])]) ).

cnf(i_0_2193,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1276]) ).

fof(i_0_2194,plain,
    ! [X6911,X6912,X6913,X6914] :
      ( ~ lattice(X6911)
      | hAPP(X6911,X6911,hAPP(X6911,fun(X6911,X6911),semilattice_sup_sup(X6911),hAPP(X6911,X6911,hAPP(X6911,fun(X6911,X6911),semilattice_sup_sup(X6911),X6912),X6913)),X6914) = hAPP(X6911,X6911,hAPP(X6911,fun(X6911,X6911),semilattice_sup_sup(X6911),X6912),hAPP(X6911,X6911,hAPP(X6911,fun(X6911,X6911),semilattice_sup_sup(X6911),X6913),X6914)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_834_inf__sup__aci_I6_J])])]) ).

fof(i_0_2195,plain,
    ! [X6915,X6916,X6917,X6918] :
      ( ~ semilattice_sup(X6915)
      | hAPP(X6915,X6915,hAPP(X6915,fun(X6915,X6915),semilattice_sup_sup(X6915),hAPP(X6915,X6915,hAPP(X6915,fun(X6915,X6915),semilattice_sup_sup(X6915),X6916),X6917)),X6918) = hAPP(X6915,X6915,hAPP(X6915,fun(X6915,X6915),semilattice_sup_sup(X6915),X6916),hAPP(X6915,X6915,hAPP(X6915,fun(X6915,X6915),semilattice_sup_sup(X6915),X6917),X6918)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_835_sup__assoc])])]) ).

fof(i_0_2196,plain,
    ! [X6907,X6908,X6909,X6910] :
      ( ~ semilattice_sup(X6907)
      | hAPP(X6907,X6907,hAPP(X6907,fun(X6907,X6907),semilattice_sup_sup(X6907),hAPP(X6907,X6907,hAPP(X6907,fun(X6907,X6907),semilattice_sup_sup(X6907),X6908),X6909)),X6910) = hAPP(X6907,X6907,hAPP(X6907,fun(X6907,X6907),semilattice_sup_sup(X6907),X6908),hAPP(X6907,X6907,hAPP(X6907,fun(X6907,X6907),semilattice_sup_sup(X6907),X6909),X6910)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_833_sup_Oassoc])])]) ).

fof(i_0_2197,plain,
    ! [X7305,X7306,X7307,X7308] :
      ( ~ lattice(X7305)
      | hAPP(X7305,X7305,hAPP(X7305,fun(X7305,X7305),semilattice_inf_inf(X7305),hAPP(X7305,X7305,hAPP(X7305,fun(X7305,X7305),semilattice_inf_inf(X7305),X7306),X7307)),X7308) = hAPP(X7305,X7305,hAPP(X7305,fun(X7305,X7305),semilattice_inf_inf(X7305),X7306),hAPP(X7305,X7305,hAPP(X7305,fun(X7305,X7305),semilattice_inf_inf(X7305),X7307),X7308)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_939_inf__sup__aci_I2_J])])]) ).

fof(i_0_2198,plain,
    ! [X7309,X7310,X7311,X7312] :
      ( ~ semilattice_inf(X7309)
      | hAPP(X7309,X7309,hAPP(X7309,fun(X7309,X7309),semilattice_inf_inf(X7309),hAPP(X7309,X7309,hAPP(X7309,fun(X7309,X7309),semilattice_inf_inf(X7309),X7310),X7311)),X7312) = hAPP(X7309,X7309,hAPP(X7309,fun(X7309,X7309),semilattice_inf_inf(X7309),X7310),hAPP(X7309,X7309,hAPP(X7309,fun(X7309,X7309),semilattice_inf_inf(X7309),X7311),X7312)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_940_inf_Oassoc])])]) ).

fof(i_0_2199,plain,
    ! [X7301,X7302,X7303,X7304] :
      ( ~ semilattice_inf(X7301)
      | hAPP(X7301,X7301,hAPP(X7301,fun(X7301,X7301),semilattice_inf_inf(X7301),hAPP(X7301,X7301,hAPP(X7301,fun(X7301,X7301),semilattice_inf_inf(X7301),X7302),X7303)),X7304) = hAPP(X7301,X7301,hAPP(X7301,fun(X7301,X7301),semilattice_inf_inf(X7301),X7302),hAPP(X7301,X7301,hAPP(X7301,fun(X7301,X7301),semilattice_inf_inf(X7301),X7303),X7304)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_938_inf__assoc])])]) ).

fof(i_0_2200,plain,
    ! [X5914,X5915,X5916,X5917] :
      ( ~ comm_semiring_1(X5914)
      | hAPP(X5914,X5914,hAPP(X5914,fun(X5914,X5914),times_times(X5914),hAPP(X5914,X5914,hAPP(X5914,fun(X5914,X5914),times_times(X5914),X5915),X5916)),X5917) = hAPP(X5914,X5914,hAPP(X5914,fun(X5914,X5914),times_times(X5914),X5915),hAPP(X5914,X5914,hAPP(X5914,fun(X5914,X5914),times_times(X5914),X5916),X5917)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])]) ).

fof(i_0_2201,plain,
    ! [X5954,X5955,X5956,X5957] :
      ( ~ ab_semigroup_mult(X5954)
      | hAPP(X5954,X5954,hAPP(X5954,fun(X5954,X5954),times_times(X5954),hAPP(X5954,X5954,hAPP(X5954,fun(X5954,X5954),times_times(X5954),X5955),X5956)),X5957) = hAPP(X5954,X5954,hAPP(X5954,fun(X5954,X5954),times_times(X5954),X5955),hAPP(X5954,X5954,hAPP(X5954,fun(X5954,X5954),times_times(X5954),X5956),X5957)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_599_ab__semigroup__mult__class_Omult__ac_I1_J])])]) ).

fof(i_0_2202,plain,
    ! [X5300,X5301,X5302,X5303] :
      ( ~ comm_semiring_1(X5300)
      | hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),X5301),X5302)),X5303) = hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),X5301),hAPP(X5300,X5300,hAPP(X5300,fun(X5300,X5300),plus_plus(X5300),X5302),X5303)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])]) ).

fof(i_0_2203,plain,
    ! [X4495,X4496,X4497,X4498] :
      ( ~ ab_semigroup_add(X4495)
      | hAPP(X4495,X4495,hAPP(X4495,fun(X4495,X4495),plus_plus(X4495),hAPP(X4495,X4495,hAPP(X4495,fun(X4495,X4495),plus_plus(X4495),X4496),X4497)),X4498) = hAPP(X4495,X4495,hAPP(X4495,fun(X4495,X4495),plus_plus(X4495),X4496),hAPP(X4495,X4495,hAPP(X4495,fun(X4495,X4495),plus_plus(X4495),X4497),X4498)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_ab__semigroup__add__class_Oadd__ac_I1_J])])]) ).

fof(i_0_2204,plain,
    ! [X5910,X5911,X5912,X5913] :
      ( ~ comm_semiring_1(X5910)
      | hAPP(X5910,X5910,hAPP(X5910,fun(X5910,X5910),times_times(X5910),X5911),hAPP(X5910,X5910,hAPP(X5910,fun(X5910,X5910),times_times(X5910),X5912),X5913)) = hAPP(X5910,X5910,hAPP(X5910,fun(X5910,X5910),times_times(X5910),hAPP(X5910,X5910,hAPP(X5910,fun(X5910,X5910),times_times(X5910),X5911),X5912)),X5913) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])])]) ).

fof(i_0_2205,plain,
    ! [X5296,X5297,X5298,X5299] :
      ( ~ comm_semiring_1(X5296)
      | hAPP(X5296,X5296,hAPP(X5296,fun(X5296,X5296),plus_plus(X5296),X5297),hAPP(X5296,X5296,hAPP(X5296,fun(X5296,X5296),plus_plus(X5296),X5298),X5299)) = hAPP(X5296,X5296,hAPP(X5296,fun(X5296,X5296),plus_plus(X5296),hAPP(X5296,X5296,hAPP(X5296,fun(X5296,X5296),plus_plus(X5296),X5297),X5298)),X5299) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])])]) ).

fof(i_0_2206,plain,
    ! [X5228,X5229] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5229),hAPP(nat,nat,suc,X5228)))
        | X5229 = X5228
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5228),X5229)) )
      & ( X5229 != X5228
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5229),hAPP(nat,nat,suc,X5228)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5228),X5229)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_421_le__less__Suc__eq])])]) ).

fof(i_0_2207,plain,
    ! [X5171,X5172] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5171),X5172))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5172),hAPP(nat,nat,suc,X5171))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5172),hAPP(nat,nat,suc,X5171)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5171),X5172)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1300])]) ).

fof(i_0_2208,plain,
    ! [X6298,X6299,X6300] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6298),X6299)),X6300) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6298),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6299),X6300)),
    inference(variable_rename,[status(thm)],[fact_703_nat__mult__assoc]) ).

fof(i_0_2209,plain,
    ! [X4710,X4711,X4712] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4710),X4711)),X4712) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4710),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4711),X4712)),
    inference(variable_rename,[status(thm)],[fact_224_nat__add__assoc]) ).

fof(i_0_2210,plain,
    ! [X7011,X7012,X7013] :
      ( ( ~ hBOOL(hAPP(fun(X7011,bool),bool,hAPP(X7011,fun(fun(X7011,bool),bool),member(X7011),X7012),hAPP(X7011,fun(X7011,bool),ord_atLeast(X7011),X7013)))
        | hBOOL(hAPP(X7011,bool,hAPP(X7011,fun(X7011,bool),ord_less_eq(X7011),X7013),X7012))
        | ~ ord(X7011) )
      & ( ~ hBOOL(hAPP(X7011,bool,hAPP(X7011,fun(X7011,bool),ord_less_eq(X7011),X7013),X7012))
        | hBOOL(hAPP(fun(X7011,bool),bool,hAPP(X7011,fun(fun(X7011,bool),bool),member(X7011),X7012),hAPP(X7011,fun(X7011,bool),ord_atLeast(X7011),X7013)))
        | ~ ord(X7011) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_860_atLeast__iff])])])]) ).

fof(i_0_2211,plain,
    ! [X5703,X5704,X5705] :
      ( ( ~ hBOOL(hAPP(fun(X5703,bool),bool,hAPP(X5703,fun(fun(X5703,bool),bool),member(X5703),X5704),hAPP(X5703,fun(X5703,bool),ord_greaterThan(X5703),X5705)))
        | hBOOL(hAPP(X5703,bool,hAPP(X5703,fun(X5703,bool),ord_less(X5703),X5705),X5704))
        | ~ ord(X5703) )
      & ( ~ hBOOL(hAPP(X5703,bool,hAPP(X5703,fun(X5703,bool),ord_less(X5703),X5705),X5704))
        | hBOOL(hAPP(fun(X5703,bool),bool,hAPP(X5703,fun(fun(X5703,bool),bool),member(X5703),X5704),hAPP(X5703,fun(X5703,bool),ord_greaterThan(X5703),X5705)))
        | ~ ord(X5703) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_538_greaterThan__iff])])])]) ).

fof(i_0_2212,plain,
    ! [X5159,X5160] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5159),X5160))
      | hAPP(nat,nat,suc,X5159) = X5160
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X5159)),X5160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_390_Suc__lessI])]) ).

cnf(i_0_2213,plain,
    ( ti(X1,esk177_3(X1,X4,X3)) = ti(X1,X2)
    | hAPP(X1,nat,X4,X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X4),X3) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]) ).

fof(i_0_2214,plain,
    ! [X7050,X7051,X7052] :
      ( ( ~ hBOOL(hAPP(fun(X7050,bool),bool,finite_finite_1(X7050),X7052))
        | hBOOL(hAPP(fun(X7050,bool),bool,finite_finite_1(X7050),hAPP(fun(X7050,bool),fun(X7050,bool),hAPP(fun(X7050,bool),fun(fun(X7050,bool),fun(X7050,bool)),semilattice_inf_inf(fun(X7050,bool)),X7052),X7051))) )
      & ( ~ hBOOL(hAPP(fun(X7050,bool),bool,finite_finite_1(X7050),X7051))
        | hBOOL(hAPP(fun(X7050,bool),bool,finite_finite_1(X7050),hAPP(fun(X7050,bool),fun(X7050,bool),hAPP(fun(X7050,bool),fun(fun(X7050,bool),fun(X7050,bool)),semilattice_inf_inf(fun(X7050,bool)),X7052),X7051))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_872_finite__Int])])]) ).

cnf(i_0_2215,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_1301]) ).

cnf(i_0_2216,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_1302]) ).

fof(i_0_2217,plain,
    ! [X5459,X5460,X5461,X5462] :
      ( ~ hBOOL(hAPP(fun(X5459,bool),bool,hAPP(fun(X5459,X5460),fun(fun(X5459,bool),bool),inj_on(X5459,X5460),X5461),X5462))
      | hAPP(fun(X5460,bool),nat,finite_card(X5460),hAPP(fun(X5459,bool),fun(X5460,bool),hAPP(fun(X5459,X5460),fun(fun(X5459,bool),fun(X5460,bool)),image(X5459,X5460),X5461),X5462)) = hAPP(fun(X5459,bool),nat,finite_card(X5459),X5462) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_483_card__image])]) ).

fof(i_0_2218,plain,
    ! [X5226,X5227] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5226),X5227))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5226)),X5227)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_420_Suc__leI])]) ).

fof(i_0_2219,plain,
    ! [X6787,X6788,X6789,X6790] :
      ( ~ hBOOL(hAPP(X6787,bool,X6789,X6790))
      | hBOOL(hAPP(X6787,bool,hAPP(fun(X6787,bool),fun(X6787,bool),hAPP(fun(X6787,bool),fun(fun(X6787,bool),fun(X6787,bool)),semilattice_sup_sup(fun(X6787,bool)),X6789),X6788),X6790)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_800_sup1I1])]) ).

fof(i_0_2220,plain,
    ! [X6680,X6681,X6682,X6683] :
      ( ( ~ hBOOL(hAPP(X6680,bool,X6682,X6683))
        | hBOOL(hAPP(X6680,bool,hAPP(fun(X6680,bool),fun(X6680,bool),hAPP(fun(X6680,bool),fun(fun(X6680,bool),fun(X6680,bool)),semilattice_sup_sup(fun(X6680,bool)),X6681),X6682),X6683)) )
      & ( ~ hBOOL(hAPP(X6680,bool,X6681,X6683))
        | hBOOL(hAPP(X6680,bool,hAPP(fun(X6680,bool),fun(X6680,bool),hAPP(fun(X6680,bool),fun(fun(X6680,bool),fun(X6680,bool)),semilattice_sup_sup(fun(X6680,bool)),X6681),X6682),X6683)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1303])])]) ).

fof(i_0_2221,plain,
    ! [X6791,X6792,X6793,X6794] :
      ( ~ hBOOL(hAPP(X6791,bool,X6793,X6794))
      | hBOOL(hAPP(X6791,bool,hAPP(fun(X6791,bool),fun(X6791,bool),hAPP(fun(X6791,bool),fun(fun(X6791,bool),fun(X6791,bool)),semilattice_sup_sup(fun(X6791,bool)),X6792),X6793),X6794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_801_sup1I2])]) ).

fof(i_0_2222,plain,
    ! [X5233] : 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)),X5233))) = hAPP(nat,nat,suc,X5233),
    inference(variable_rename,[status(thm)],[fact_425_card__Collect__le__nat]) ).

fof(i_0_2223,plain,
    ! [X5332,X5333,X5334,X5335] :
      ( ~ hBOOL(hAPP(fun(X5333,bool),bool,finite_finite_1(X5333),X5335))
      | hBOOL(hAPP(fun(X5332,bool),bool,finite_finite_1(X5332),hAPP(fun(X5333,bool),fun(X5332,bool),hAPP(fun(X5333,X5332),fun(fun(X5333,bool),fun(X5332,bool)),image(X5333,X5332),X5334),X5335))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_459_finite__imageI])]) ).

cnf(i_0_2224,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_1304]) ).

fof(i_0_2225,plain,
    ! [X5187,X5188] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5187),hAPP(nat,nat,suc,X5188)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5187),X5188))
        | X5187 = hAPP(nat,nat,suc,X5188) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5187),X5188))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5187),hAPP(nat,nat,suc,X5188))) )
      & ( X5187 != hAPP(nat,nat,suc,X5188)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5187),hAPP(nat,nat,suc,X5188))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_404_le__Suc__eq])])]) ).

fof(i_0_2226,plain,
    ! [X5181,X5182] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5181),hAPP(nat,nat,suc,X5182)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5181),X5182))
      | X5181 = hAPP(nat,nat,suc,X5182) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1305])]) ).

fof(i_0_2227,plain,
    ! [X5268,X5269] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5268)),X5269))
      | X5269 = hAPP(nat,nat,suc,esk93_2(X5268,X5269)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_438_Suc__le__D])])]) ).

fof(i_0_2228,plain,
    ! [X5242,X5243,X5244] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk87_3(X5242,X5243,X5244)),X5244))
        | hBOOL(hAPP(nat,bool,X5242,X5243))
        | ~ hBOOL(hAPP(nat,bool,X5242,X5244))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5243),X5244)) )
      & ( hBOOL(hAPP(nat,bool,X5242,hAPP(nat,nat,suc,esk87_3(X5242,X5243,X5244))))
        | hBOOL(hAPP(nat,bool,X5242,X5243))
        | ~ hBOOL(hAPP(nat,bool,X5242,X5244))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5243),X5244)) )
      & ( ~ hBOOL(hAPP(nat,bool,X5242,esk87_3(X5242,X5243,X5244)))
        | hBOOL(hAPP(nat,bool,X5242,X5243))
        | ~ hBOOL(hAPP(nat,bool,X5242,X5244))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5243),X5244)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_430_inc__induct])])])]) ).

fof(i_0_2229,plain,
    ! [X4268,X4269,X4270] :
      ( ( hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less_eq(X4268),X4269),X4270))
        | ~ hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less(X4268),X4269),X4270))
        | ~ preorder(X4268) )
      & ( ~ hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less_eq(X4268),X4270),X4269))
        | ~ hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less(X4268),X4269),X4270))
        | ~ preorder(X4268) )
      & ( ~ hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less_eq(X4268),X4269),X4270))
        | hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less_eq(X4268),X4270),X4269))
        | hBOOL(hAPP(X4268,bool,hAPP(X4268,fun(X4268,bool),ord_less(X4268),X4269),X4270))
        | ~ preorder(X4268) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])])])]) ).

fof(i_0_2230,plain,
    ! [X4916] : 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)),X4916))) = X4916,
    inference(variable_rename,[status(thm)],[fact_291_card__Collect__less__nat]) ).

fof(i_0_2231,plain,
    ! [X5198,X5199,X5201,X5202,X5203] :
      ( ( X5198 = hAPP(nat,nat,suc,esk85_2(X5198,X5199))
        | X5198 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5198),hAPP(nat,nat,suc,X5199))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X5198,X5199)),X5199))
        | X5198 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5198),hAPP(nat,nat,suc,X5199))) )
      & ( X5201 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5201),hAPP(nat,nat,suc,X5202))) )
      & ( X5201 != hAPP(nat,nat,suc,X5203)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5203),X5202))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5201),hAPP(nat,nat,suc,X5202))) ) ),
    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_410_less__Suc__eq__0__disj])])])])])]) ).

fof(i_0_2232,plain,
    ! [X4812,X4813,X4814] :
      ( ( hBOOL(hAPP(fun(X4812,bool),bool,hAPP(X4812,fun(fun(X4812,bool),bool),member(X4812),esk60_3(X4812,X4813,X4814)),X4814))
        | hBOOL(hAPP(fun(X4812,bool),bool,hAPP(fun(X4812,bool),fun(fun(X4812,bool),bool),ord_less_eq(fun(X4812,bool)),X4814),X4813)) )
      & ( ~ hBOOL(hAPP(fun(X4812,bool),bool,hAPP(X4812,fun(fun(X4812,bool),bool),member(X4812),esk60_3(X4812,X4813,X4814)),X4813))
        | hBOOL(hAPP(fun(X4812,bool),bool,hAPP(fun(X4812,bool),fun(fun(X4812,bool),bool),ord_less_eq(fun(X4812,bool)),X4814),X4813)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_259_subsetI])])])]) ).

fof(i_0_2233,plain,
    ! [X6449,X6450,X6451,X6452,X6453,X6454,X6455,X6456,X6457] :
      ( hAPP(fun(X6449,X6450),fun(X6449,X6451),hAPP(fun(X6450,X6451),fun(fun(X6449,X6450),fun(X6449,X6451)),comp(X6450,X6451,X6449),X6453),X6454) != hAPP(fun(X6449,X6452),fun(X6449,X6451),hAPP(fun(X6452,X6451),fun(fun(X6449,X6452),fun(X6449,X6451)),comp(X6452,X6451,X6449),X6455),X6456)
      | hAPP(X6450,X6451,X6453,hAPP(X6449,X6450,X6454,X6457)) = hAPP(X6452,X6451,X6455,hAPP(X6449,X6452,X6456,X6457)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_732_o__eq__elim])])]) ).

fof(i_0_2234,plain,
    ! [X6440,X6441,X6442,X6443,X6444,X6445,X6446,X6447,X6448] :
      ( hAPP(fun(X6440,X6441),fun(X6440,X6442),hAPP(fun(X6441,X6442),fun(fun(X6440,X6441),fun(X6440,X6442)),comp(X6441,X6442,X6440),X6445),X6446) != hAPP(fun(X6440,X6443),fun(X6440,X6442),hAPP(fun(X6443,X6442),fun(fun(X6440,X6443),fun(X6440,X6442)),comp(X6443,X6442,X6440),X6447),X6448)
      | hAPP(X6441,X6442,X6445,hAPP(X6440,X6441,X6446,X6444)) = hAPP(X6443,X6442,X6447,hAPP(X6440,X6443,X6448,X6444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_731_o__eq__dest])]) ).

fof(i_0_2235,plain,
    ! [X5513,X5514] :
      ( ~ hBOOL(hAPP(fun(X5513,bool),bool,finite_finite_1(X5513),top_top(fun(X5513,bool))))
      | ~ hBOOL(hAPP(fun(X5513,bool),bool,hAPP(fun(X5513,X5513),fun(fun(X5513,bool),bool),inj_on(X5513,X5513),X5514),top_top(fun(X5513,bool))))
      | hAPP(fun(X5513,bool),fun(X5513,bool),hAPP(fun(X5513,X5513),fun(fun(X5513,bool),fun(X5513,bool)),image(X5513,X5513),X5514),top_top(fun(X5513,bool))) = top_top(fun(X5513,bool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_finite__UNIV__inj__surj])]) ).

fof(i_0_2236,plain,
    ! [X7498,X7499,X7500,X7501] :
      ( ( hAPP(fun(X7498,bool),nat,hAPP(fun(X7498,nat),fun(fun(X7498,bool),nat),big_co1399186613setsum(X7498,nat),X7499),X7500) != zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7498,bool),bool,hAPP(X7498,fun(fun(X7498,bool),bool),member(X7498),X7501),X7500))
        | hAPP(X7498,nat,X7499,X7501) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7498,bool),bool,finite_finite_1(X7498),X7500)) )
      & ( hBOOL(hAPP(fun(X7498,bool),bool,hAPP(X7498,fun(fun(X7498,bool),bool),member(X7498),esk174_3(X7498,X7499,X7500)),X7500))
        | hAPP(fun(X7498,bool),nat,hAPP(fun(X7498,nat),fun(fun(X7498,bool),nat),big_co1399186613setsum(X7498,nat),X7499),X7500) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7498,bool),bool,finite_finite_1(X7498),X7500)) )
      & ( hAPP(X7498,nat,X7499,esk174_3(X7498,X7499,X7500)) != zero_zero(nat)
        | hAPP(fun(X7498,bool),nat,hAPP(fun(X7498,nat),fun(fun(X7498,bool),nat),big_co1399186613setsum(X7498,nat),X7499),X7500) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X7498,bool),bool,finite_finite_1(X7498),X7500)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_986_setsum__eq__0__iff])])])])]) ).

fof(i_0_2237,plain,
    ! [X5169,X5170] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5169),hAPP(nat,nat,suc,X5170)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5169),X5170))
        | X5169 = X5170 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5169),X5170))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5169),hAPP(nat,nat,suc,X5170))) )
      & ( X5169 != X5170
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5169),hAPP(nat,nat,suc,X5170))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_395_less__Suc__eq])])]) ).

fof(i_0_2238,plain,
    ! [X5165,X5166] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5165),hAPP(nat,nat,suc,X5166)))
        | X5165 = X5166
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5165),X5166)) )
      & ( X5165 != X5166
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5165),hAPP(nat,nat,suc,X5166)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5165),X5166)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1307])])]) ).

fof(i_0_2239,plain,
    ! [X5163,X5164] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5163),X5164))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5163),hAPP(nat,nat,suc,X5164)))
      | X5164 = X5163 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])]) ).

fof(i_0_2240,plain,
    ! [X5154,X5155] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5154),hAPP(nat,nat,suc,X5155)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5154),X5155))
      | X5154 = X5155 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1309])]) ).

fof(i_0_2241,plain,
    ! [X5220,X5221] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5220),hAPP(nat,nat,suc,X5221)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5220),X5221)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5220),X5221))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5220),hAPP(nat,nat,suc,X5221))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_417_less__Suc__eq__le])]) ).

cnf(i_0_2242,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_1310]) ).

cnf(i_0_2243,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_1311]) ).

cnf(i_0_2244,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_1312]) ).

cnf(i_0_2245,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_1313]) ).

cnf(i_0_2246,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X4)),X5),X6) = ti(X2,X4),
    inference(split_conjunct,[status(thm)],[i_0_1314]) ).

fof(i_0_2247,plain,
    ! [X5191] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5191)),X5191)),
    inference(variable_rename,[status(thm)],[i_0_1315]) ).

fof(i_0_2248,plain,
    ! [X5970,X5971,X5972] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5970)),X5971) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5970)),X5972)
        | X5971 = X5972 )
      & ( X5971 != X5972
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5970)),X5971) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X5970)),X5972) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_606_Suc__mult__cancel1])]) ).

fof(i_0_2249,plain,
    ! [X4628,X4629,X4630] :
      ( ~ hBOOL(hAPP(fun(X4628,bool),bool,hAPP(fun(X4628,bool),fun(fun(X4628,bool),bool),ord_less(fun(X4628,bool)),X4629),X4630))
      | hBOOL(hAPP(fun(X4628,bool),bool,hAPP(fun(X4628,bool),fun(fun(X4628,bool),bool),ord_less_eq(fun(X4628,bool)),X4629),X4630)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_198_psubset__imp__subset])]) ).

fof(i_0_2250,plain,
    ! [X4940,X4942,X4943,X4944] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4940))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4942),X4940))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4942),esk71_1(X4940))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk72_2(X4943,X4944)),X4943))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4943)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk72_2(X4943,X4944)),X4944))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4943)) ) ),
    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_303_finite__nat__set__iff__bounded__le])])])])])]) ).

fof(i_0_2251,plain,
    ! [X4946,X4948,X4949,X4950] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4946))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4948),X4946))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4948),esk73_1(X4946))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X4949,X4950)),X4949))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4949)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk74_2(X4949,X4950)),X4950))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X4949)) ) ),
    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_304_finite__nat__set__iff__bounded])])])])])]) ).

fof(i_0_2252,plain,
    ! [X5602,X5603] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X5602),X5603)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X5602)),hAPP(nat,nat,suc,X5603)),
    inference(variable_rename,[status(thm)],[fact_515_image__Suc__atLeastLessThan]) ).

fof(i_0_2253,plain,
    ! [X6642,X6643] : hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X6642),X6643)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X6642)),hAPP(nat,nat,suc,X6643)),
    inference(variable_rename,[status(thm)],[fact_766_image__Suc__atLeastAtMost]) ).

fof(i_0_2254,plain,
    ! [X5116,X5117,X5119] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk80_2(X5116,X5117)),X5116))
        | ~ hBOOL(hAPP(nat,bool,X5117,X5116))
        | hBOOL(hAPP(nat,bool,X5117,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5119),esk80_2(X5116,X5117)))
        | ~ hBOOL(hAPP(nat,bool,X5117,X5119))
        | ~ hBOOL(hAPP(nat,bool,X5117,X5116))
        | hBOOL(hAPP(nat,bool,X5117,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X5117,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk80_2(X5116,X5117)),one_one(nat))))
        | ~ hBOOL(hAPP(nat,bool,X5117,X5116))
        | hBOOL(hAPP(nat,bool,X5117,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_1316])])])])]) ).

cnf(i_0_2255,plain,
    ( 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))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk128_4(X1,X2,X3,X4))) != ti(X2,esk128_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1317]) ).

fof(i_0_2256,plain,
    ! [X5515,X5516] :
      ( ~ hBOOL(hAPP(fun(X5515,bool),bool,finite_finite_1(X5515),top_top(fun(X5515,bool))))
      | hAPP(fun(X5515,bool),fun(X5515,bool),hAPP(fun(X5515,X5515),fun(fun(X5515,bool),fun(X5515,bool)),image(X5515,X5515),X5516),top_top(fun(X5515,bool))) != top_top(fun(X5515,bool))
      | hBOOL(hAPP(fun(X5515,bool),bool,hAPP(fun(X5515,X5515),fun(fun(X5515,bool),bool),inj_on(X5515,X5515),X5516),top_top(fun(X5515,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_finite__UNIV__surj__inj])]) ).

fof(i_0_2257,plain,
    ! [X4085,X4086,X4087,X4088] :
      ( ~ preorder(X4085)
      | ~ hBOOL(hAPP(X4085,bool,hAPP(X4085,fun(X4085,bool),ord_less(X4085),X4087),X4088))
      | ~ hBOOL(hAPP(X4085,bool,hAPP(X4085,fun(X4085,bool),ord_less(X4085),X4088),X4087))
      | hBOOL(X4086) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_order__less__imp__triv])])]) ).

fof(i_0_2258,plain,
    ! [X4098,X4099,X4100] :
      ( ~ preorder(X4098)
      | ~ hBOOL(hAPP(X4098,bool,hAPP(X4098,fun(X4098,bool),ord_less(X4098),X4099),X4100))
      | ~ hBOOL(hAPP(X4098,bool,hAPP(X4098,fun(X4098,bool),ord_less(X4098),X4100),X4099)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1318])])]) ).

fof(i_0_2259,plain,
    ! [X4095,X4096,X4097] :
      ( ~ preorder(X4095)
      | ~ hBOOL(hAPP(X4095,bool,hAPP(X4095,fun(X4095,bool),ord_less(X4095),X4096),X4097))
      | ~ hBOOL(hAPP(X4095,bool,hAPP(X4095,fun(X4095,bool),ord_less(X4095),X4097),X4096)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1319])])]) ).

fof(i_0_2260,plain,
    ! [X4082,X4083,X4084] :
      ( ~ preorder(X4082)
      | ~ hBOOL(hAPP(X4082,bool,hAPP(X4082,fun(X4082,bool),ord_less(X4082),X4083),X4084))
      | ~ hBOOL(hAPP(X4082,bool,hAPP(X4082,fun(X4082,bool),ord_less(X4082),X4084),X4083)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1320])])]) ).

fof(i_0_2261,plain,
    ! [X4052,X4053,X4054] :
      ( ~ preorder(X4052)
      | ~ hBOOL(hAPP(X4052,bool,hAPP(X4052,fun(X4052,bool),ord_less(X4052),X4053),X4054))
      | ~ hBOOL(hAPP(X4052,bool,hAPP(X4052,fun(X4052,bool),ord_less(X4052),X4054),X4053)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1321])])]) ).

fof(i_0_2262,plain,
    ! [X4259,X4260,X4261] :
      ( ( hBOOL(hAPP(X4259,bool,hAPP(X4259,fun(X4259,bool),ord_less_eq(X4259),X4260),X4261))
        | hBOOL(hAPP(X4259,bool,hAPP(X4259,fun(X4259,bool),ord_less(X4259),X4261),X4260))
        | ~ linorder(X4259) )
      & ( ~ hBOOL(hAPP(X4259,bool,hAPP(X4259,fun(X4259,bool),ord_less(X4259),X4261),X4260))
        | ~ hBOOL(hAPP(X4259,bool,hAPP(X4259,fun(X4259,bool),ord_less_eq(X4259),X4260),X4261))
        | ~ linorder(X4259) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1322])])])]) ).

fof(i_0_2263,plain,
    ! [X4289,X4290,X4291] :
      ( ~ linorder(X4289)
      | ~ hBOOL(hAPP(X4289,bool,hAPP(X4289,fun(X4289,bool),ord_less_eq(X4289),X4290),X4291))
      | ~ hBOOL(hAPP(X4289,bool,hAPP(X4289,fun(X4289,bool),ord_less(X4289),X4291),X4290)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])])]) ).

fof(i_0_2264,plain,
    ! [X4256,X4257,X4258] :
      ( ( hBOOL(hAPP(X4256,bool,hAPP(X4256,fun(X4256,bool),ord_less(X4256),X4257),X4258))
        | hBOOL(hAPP(X4256,bool,hAPP(X4256,fun(X4256,bool),ord_less_eq(X4256),X4258),X4257))
        | ~ linorder(X4256) )
      & ( ~ hBOOL(hAPP(X4256,bool,hAPP(X4256,fun(X4256,bool),ord_less_eq(X4256),X4258),X4257))
        | ~ hBOOL(hAPP(X4256,bool,hAPP(X4256,fun(X4256,bool),ord_less(X4256),X4257),X4258))
        | ~ linorder(X4256) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1324])])])]) ).

fof(i_0_2265,plain,
    ! [X4079,X4080,X4081] :
      ( ~ order(X4079)
      | ~ hBOOL(hAPP(X4079,bool,hAPP(X4079,fun(X4079,bool),ord_less(X4079),X4080),X4081))
      | ~ hBOOL(hAPP(X4079,bool,hAPP(X4079,fun(X4079,bool),ord_less(X4079),X4081),X4080)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])])]) ).

fof(i_0_2266,plain,
    ! [X5183,X5184] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5183),X5184))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5183),hAPP(nat,nat,suc,X5184))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_402_le__SucI])]) ).

fof(i_0_2267,plain,
    ! [X5224,X5225] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5224),X5225))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5224),hAPP(nat,nat,suc,X5225))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_419_le__imp__less__Suc])]) ).

fof(i_0_2268,plain,
    ! [X5161,X5162] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5161),X5162))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5161),hAPP(nat,nat,suc,X5162))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_391_less__SucI])]) ).

fof(i_0_2269,plain,
    ! [X6855,X6856,X6857,X6858,X6859] :
      ( ~ lattice(X6856)
      | hAPP(X6855,X6856,hAPP(fun(X6855,X6856),fun(X6855,X6856),hAPP(fun(X6855,X6856),fun(fun(X6855,X6856),fun(X6855,X6856)),semilattice_sup_sup(fun(X6855,X6856)),X6857),X6858),X6859) = hAPP(X6856,X6856,hAPP(X6856,fun(X6856,X6856),semilattice_sup_sup(X6856),hAPP(X6855,X6856,X6857,X6859)),hAPP(X6855,X6856,X6858,X6859)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_817_sup__fun__def])])]) ).

fof(i_0_2270,plain,
    ! [X6850,X6851,X6852,X6853,X6854] :
      ( ~ lattice(X6851)
      | hAPP(X6850,X6851,hAPP(fun(X6850,X6851),fun(X6850,X6851),hAPP(fun(X6850,X6851),fun(fun(X6850,X6851),fun(X6850,X6851)),semilattice_sup_sup(fun(X6850,X6851)),X6852),X6853),X6854) = hAPP(X6851,X6851,hAPP(X6851,fun(X6851,X6851),semilattice_sup_sup(X6851),hAPP(X6850,X6851,X6852,X6854)),hAPP(X6850,X6851,X6853,X6854)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_816_sup__apply])])]) ).

fof(i_0_2271,plain,
    ! [X7343,X7344,X7345,X7346,X7347] :
      ( ~ lattice(X7344)
      | hAPP(X7343,X7344,hAPP(fun(X7343,X7344),fun(X7343,X7344),hAPP(fun(X7343,X7344),fun(fun(X7343,X7344),fun(X7343,X7344)),semilattice_inf_inf(fun(X7343,X7344)),X7345),X7346),X7347) = hAPP(X7344,X7344,hAPP(X7344,fun(X7344,X7344),semilattice_inf_inf(X7344),hAPP(X7343,X7344,X7345,X7347)),hAPP(X7343,X7344,X7346,X7347)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_950_inf__fun__def])])]) ).

fof(i_0_2272,plain,
    ! [X7296,X7297,X7298,X7299,X7300] :
      ( ~ lattice(X7297)
      | hAPP(X7296,X7297,hAPP(fun(X7296,X7297),fun(X7296,X7297),hAPP(fun(X7296,X7297),fun(fun(X7296,X7297),fun(X7296,X7297)),semilattice_inf_inf(fun(X7296,X7297)),X7298),X7299),X7300) = hAPP(X7297,X7297,hAPP(X7297,fun(X7297,X7297),semilattice_inf_inf(X7297),hAPP(X7296,X7297,X7298,X7300)),hAPP(X7296,X7297,X7299,X7300)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_937_inf__apply])])]) ).

fof(i_0_2273,plain,
    ! [X6307,X6308,X6309] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6309),X6307) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6309),X6308)
        | X6307 = X6308
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6309)) )
      & ( X6307 != X6308
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6309),X6307) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6309),X6308)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X6309)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_706_nat__mult__eq__cancel1])])]) ).

fof(i_0_2274,plain,
    ! [X5112] :
      ( ~ linordered_semidom(X5112)
      | hBOOL(hAPP(X5112,bool,hAPP(X5112,fun(X5112,bool),ord_less(X5112),zero_zero(X5112)),hAPP(X5112,X5112,hAPP(X5112,fun(X5112,X5112),plus_plus(X5112),one_one(X5112)),one_one(X5112)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_zero__less__two])]) ).

fof(i_0_2275,plain,
    ! [X4727,X4728] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4727),X4728))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4728),X4727))
      | X4727 = X4728 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_le__antisym])]) ).

cnf(i_0_2276,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_1311]) ).

cnf(i_0_2277,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_1326]) ).

cnf(i_0_2278,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_1327]) ).

cnf(i_0_2279,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_1328]) ).

cnf(i_0_2280,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_1329]) ).

cnf(i_0_2281,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_1330]) ).

fof(i_0_2282,plain,
    ! [X6141,X6142] :
      ( ~ comm_semiring_1(X6141)
      | hAPP(X6141,X6141,hAPP(X6141,fun(X6141,X6141),plus_plus(X6141),X6142),X6142) = hAPP(X6141,X6141,hAPP(X6141,fun(X6141,X6141),times_times(X6141),hAPP(X6141,X6141,hAPP(X6141,fun(X6141,X6141),plus_plus(X6141),one_one(X6141)),one_one(X6141))),X6142) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])]) ).

fof(i_0_2283,plain,
    ! [X6005,X6006] :
      ( ~ linordered_ring(X6005)
      | hBOOL(hAPP(X6005,bool,hAPP(X6005,fun(X6005,bool),ord_less_eq(X6005),zero_zero(X6005)),hAPP(X6005,X6005,hAPP(X6005,fun(X6005,X6005),times_times(X6005),X6006),X6006))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_619_zero__le__square])])]) ).

fof(i_0_2284,plain,
    ! [X4410,X4411] :
      ( ~ linordered_semidom(X4410)
      | hBOOL(hAPP(X4410,bool,hAPP(X4410,fun(X4410,bool),ord_less(X4410),X4411),hAPP(X4410,X4410,hAPP(X4410,fun(X4410,X4410),plus_plus(X4410),X4411),one_one(X4410)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_less__add__one])])]) ).

fof(i_0_2285,plain,
    ! [X6899,X6900,X6901,X6902] :
      ( ~ lattice(X6899)
      | hAPP(X6899,X6899,hAPP(X6899,fun(X6899,X6899),semilattice_sup_sup(X6899),X6900),hAPP(X6899,X6899,hAPP(X6899,fun(X6899,X6899),semilattice_sup_sup(X6899),X6901),X6902)) = hAPP(X6899,X6899,hAPP(X6899,fun(X6899,X6899),semilattice_sup_sup(X6899),X6901),hAPP(X6899,X6899,hAPP(X6899,fun(X6899,X6899),semilattice_sup_sup(X6899),X6900),X6902)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_831_inf__sup__aci_I7_J])])]) ).

fof(i_0_2286,plain,
    ! [X6903,X6904,X6905,X6906] :
      ( ~ semilattice_sup(X6903)
      | hAPP(X6903,X6903,hAPP(X6903,fun(X6903,X6903),semilattice_sup_sup(X6903),X6904),hAPP(X6903,X6903,hAPP(X6903,fun(X6903,X6903),semilattice_sup_sup(X6903),X6905),X6906)) = hAPP(X6903,X6903,hAPP(X6903,fun(X6903,X6903),semilattice_sup_sup(X6903),X6905),hAPP(X6903,X6903,hAPP(X6903,fun(X6903,X6903),semilattice_sup_sup(X6903),X6904),X6906)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_832_sup__left__commute])])]) ).

fof(i_0_2287,plain,
    ! [X6895,X6896,X6897,X6898] :
      ( ~ semilattice_sup(X6895)
      | hAPP(X6895,X6895,hAPP(X6895,fun(X6895,X6895),semilattice_sup_sup(X6895),X6896),hAPP(X6895,X6895,hAPP(X6895,fun(X6895,X6895),semilattice_sup_sup(X6895),X6897),X6898)) = hAPP(X6895,X6895,hAPP(X6895,fun(X6895,X6895),semilattice_sup_sup(X6895),X6897),hAPP(X6895,X6895,hAPP(X6895,fun(X6895,X6895),semilattice_sup_sup(X6895),X6896),X6898)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_830_sup_Oleft__commute])])]) ).

fof(i_0_2288,plain,
    ! [X7317,X7318,X7319,X7320] :
      ( ~ lattice(X7317)
      | hAPP(X7317,X7317,hAPP(X7317,fun(X7317,X7317),semilattice_inf_inf(X7317),X7318),hAPP(X7317,X7317,hAPP(X7317,fun(X7317,X7317),semilattice_inf_inf(X7317),X7319),X7320)) = hAPP(X7317,X7317,hAPP(X7317,fun(X7317,X7317),semilattice_inf_inf(X7317),X7319),hAPP(X7317,X7317,hAPP(X7317,fun(X7317,X7317),semilattice_inf_inf(X7317),X7318),X7320)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_942_inf__sup__aci_I3_J])])]) ).

fof(i_0_2289,plain,
    ! [X7321,X7322,X7323,X7324] :
      ( ~ semilattice_inf(X7321)
      | hAPP(X7321,X7321,hAPP(X7321,fun(X7321,X7321),semilattice_inf_inf(X7321),X7322),hAPP(X7321,X7321,hAPP(X7321,fun(X7321,X7321),semilattice_inf_inf(X7321),X7323),X7324)) = hAPP(X7321,X7321,hAPP(X7321,fun(X7321,X7321),semilattice_inf_inf(X7321),X7323),hAPP(X7321,X7321,hAPP(X7321,fun(X7321,X7321),semilattice_inf_inf(X7321),X7322),X7324)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_943_inf_Oleft__commute])])]) ).

fof(i_0_2290,plain,
    ! [X7313,X7314,X7315,X7316] :
      ( ~ semilattice_inf(X7313)
      | hAPP(X7313,X7313,hAPP(X7313,fun(X7313,X7313),semilattice_inf_inf(X7313),X7314),hAPP(X7313,X7313,hAPP(X7313,fun(X7313,X7313),semilattice_inf_inf(X7313),X7315),X7316)) = hAPP(X7313,X7313,hAPP(X7313,fun(X7313,X7313),semilattice_inf_inf(X7313),X7315),hAPP(X7313,X7313,hAPP(X7313,fun(X7313,X7313),semilattice_inf_inf(X7313),X7314),X7316)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_941_inf__left__commute])])]) ).

fof(i_0_2291,plain,
    ! [X5906,X5907,X5908,X5909] :
      ( ~ comm_semiring_1(X5906)
      | hAPP(X5906,X5906,hAPP(X5906,fun(X5906,X5906),times_times(X5906),X5907),hAPP(X5906,X5906,hAPP(X5906,fun(X5906,X5906),times_times(X5906),X5908),X5909)) = hAPP(X5906,X5906,hAPP(X5906,fun(X5906,X5906),times_times(X5906),X5908),hAPP(X5906,X5906,hAPP(X5906,fun(X5906,X5906),times_times(X5906),X5907),X5909)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])]) ).

fof(i_0_2292,plain,
    ! [X5292,X5293,X5294,X5295] :
      ( ~ comm_semiring_1(X5292)
      | hAPP(X5292,X5292,hAPP(X5292,fun(X5292,X5292),plus_plus(X5292),X5293),hAPP(X5292,X5292,hAPP(X5292,fun(X5292,X5292),plus_plus(X5292),X5294),X5295)) = hAPP(X5292,X5292,hAPP(X5292,fun(X5292,X5292),plus_plus(X5292),X5294),hAPP(X5292,X5292,hAPP(X5292,fun(X5292,X5292),plus_plus(X5292),X5293),X5295)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])]) ).

fof(i_0_2293,plain,
    ! [X6919,X6920,X6921] :
      ( ~ lattice(X6919)
      | hBOOL(hAPP(X6919,bool,hAPP(X6919,fun(X6919,bool),ord_less_eq(X6919),X6920),hAPP(X6919,X6919,hAPP(X6919,fun(X6919,X6919),semilattice_sup_sup(X6919),X6920),X6921))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_836_inf__sup__ord_I3_J])])]) ).

fof(i_0_2294,plain,
    ! [X6922,X6923,X6924] :
      ( ~ semilattice_sup(X6922)
      | hBOOL(hAPP(X6922,bool,hAPP(X6922,fun(X6922,bool),ord_less_eq(X6922),X6923),hAPP(X6922,X6922,hAPP(X6922,fun(X6922,X6922),semilattice_sup_sup(X6922),X6923),X6924))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_837_sup__ge1])])]) ).

fof(i_0_2295,plain,
    ! [X6925,X6926,X6927] :
      ( ~ lattice(X6925)
      | hBOOL(hAPP(X6925,bool,hAPP(X6925,fun(X6925,bool),ord_less_eq(X6925),X6926),hAPP(X6925,X6925,hAPP(X6925,fun(X6925,X6925),semilattice_sup_sup(X6925),X6927),X6926))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_838_inf__sup__ord_I4_J])])]) ).

fof(i_0_2296,plain,
    ! [X6928,X6929,X6930] :
      ( ~ semilattice_sup(X6928)
      | hBOOL(hAPP(X6928,bool,hAPP(X6928,fun(X6928,bool),ord_less_eq(X6928),X6929),hAPP(X6928,X6928,hAPP(X6928,fun(X6928,X6928),semilattice_sup_sup(X6928),X6930),X6929))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_839_sup__ge2])])]) ).

cnf(i_0_2297,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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_1331]) ).

cnf(i_0_2298,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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_1332]) ).

cnf(i_0_2299,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),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_1333]) ).

cnf(i_0_2300,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = ti(fun(X1,bool),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(split_conjunct,[status(thm)],[i_0_1334]) ).

cnf(i_0_2301,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2) = ti(fun(X1,bool),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(split_conjunct,[status(thm)],[i_0_1335]) ).

fof(i_0_2302,plain,
    ! [X4427,X4428,X4429] :
      ( ( hBOOL(hAPP(X4427,bool,hAPP(X4427,fun(X4427,bool),ord_less(X4427),esk37_3(X4427,X4428,X4429)),X4429))
        | hBOOL(hAPP(X4427,bool,hAPP(X4427,fun(X4427,bool),ord_less_eq(X4427),X4429),X4428))
        | ~ dense_linorder(X4427) )
      & ( ~ hBOOL(hAPP(X4427,bool,hAPP(X4427,fun(X4427,bool),ord_less_eq(X4427),esk37_3(X4427,X4428,X4429)),X4428))
        | hBOOL(hAPP(X4427,bool,hAPP(X4427,fun(X4427,bool),ord_less_eq(X4427),X4429),X4428))
        | ~ dense_linorder(X4427) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_155_dense__le])])])])]) ).

fof(i_0_2303,plain,
    ! [X5649,X5650] :
      ( ( hAPP(fun(X5649,bool),fun(nat,bool),hAPP(fun(X5649,nat),fun(fun(X5649,bool),fun(nat,bool)),image(X5649,nat),esk122_2(X5649,X5650)),X5650) = 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)),esk123_2(X5649,X5650)))
        | ~ hBOOL(hAPP(fun(X5649,bool),bool,finite_finite_1(X5649),X5650)) )
      & ( hBOOL(hAPP(fun(X5649,bool),bool,hAPP(fun(X5649,nat),fun(fun(X5649,bool),bool),inj_on(X5649,nat),esk122_2(X5649,X5650)),X5650))
        | ~ hBOOL(hAPP(fun(X5649,bool),bool,finite_finite_1(X5649),X5650)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_524_finite__imp__inj__to__nat__seg])])])])]) ).

fof(i_0_2304,plain,
    ! [X5113,X5114] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5113,bool),nat,finite_card(X5113),X5114)))
      | hBOOL(hAPP(fun(X5113,bool),bool,finite_finite_1(X5113),X5114)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_365_card__ge__0__finite])]) ).

fof(i_0_2305,plain,
    ! [X4920,X4921,X4922] :
      ( ~ hBOOL(hAPP(fun(X4920,bool),bool,hAPP(fun(X4920,bool),fun(fun(X4920,bool),bool),ord_less_eq(fun(X4920,bool)),X4921),X4922))
      | ~ hBOOL(hAPP(fun(X4920,bool),bool,finite_finite_1(X4920),X4922))
      | hBOOL(hAPP(fun(X4920,bool),bool,finite_finite_1(X4920),X4921)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_finite__subset])]) ).

fof(i_0_2306,plain,
    ! [X4917,X4918,X4919] :
      ( ~ hBOOL(hAPP(fun(X4917,bool),bool,finite_finite_1(X4917),X4919))
      | ~ hBOOL(hAPP(fun(X4917,bool),bool,hAPP(fun(X4917,bool),fun(fun(X4917,bool),bool),ord_less_eq(fun(X4917,bool)),X4918),X4919))
      | hBOOL(hAPP(fun(X4917,bool),bool,finite_finite_1(X4917),X4918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_292_rev__finite__subset])]) ).

fof(i_0_2307,plain,
    ! [X6744,X6745,X6746] : hAPP(fun(X6744,bool),fun(X6744,bool),hAPP(fun(X6744,bool),fun(fun(X6744,bool),fun(X6744,bool)),semilattice_sup_sup(fun(X6744,bool)),X6745),hAPP(fun(X6744,bool),fun(X6744,bool),hAPP(fun(X6744,bool),fun(fun(X6744,bool),fun(X6744,bool)),semilattice_sup_sup(fun(X6744,bool)),X6745),X6746)) = hAPP(fun(X6744,bool),fun(X6744,bool),hAPP(fun(X6744,bool),fun(fun(X6744,bool),fun(X6744,bool)),semilattice_sup_sup(fun(X6744,bool)),X6745),X6746),
    inference(variable_rename,[status(thm)],[fact_794_Un__left__absorb]) ).

fof(i_0_2308,plain,
    ! [X7183,X7184,X7185] : hAPP(fun(X7183,bool),fun(X7183,bool),hAPP(fun(X7183,bool),fun(fun(X7183,bool),fun(X7183,bool)),semilattice_inf_inf(fun(X7183,bool)),X7184),hAPP(fun(X7183,bool),fun(X7183,bool),hAPP(fun(X7183,bool),fun(fun(X7183,bool),fun(X7183,bool)),semilattice_inf_inf(fun(X7183,bool)),X7184),X7185)) = hAPP(fun(X7183,bool),fun(X7183,bool),hAPP(fun(X7183,bool),fun(fun(X7183,bool),fun(X7183,bool)),semilattice_inf_inf(fun(X7183,bool)),X7184),X7185),
    inference(variable_rename,[status(thm)],[fact_905_Int__left__absorb]) ).

fof(i_0_2309,plain,
    ! [X5865] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5865),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5865),X5865))),
    inference(variable_rename,[status(thm)],[fact_572_le__square]) ).

fof(i_0_2310,plain,
    ! [X4770,X4771] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4770),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4770),X4771))),
    inference(variable_rename,[status(thm)],[fact_248_le__add1]) ).

fof(i_0_2311,plain,
    ! [X4768,X4769] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4768),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4769),X4768))),
    inference(variable_rename,[status(thm)],[fact_247_le__add2]) ).

fof(i_0_2312,plain,
    ! [X4702,X4703,X4704] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | X4703 = X4704
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4703),X4704)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | X4703 = X4704
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4703),X4704)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4703),X4704)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4703),X4704)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | X4703 = X4704
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | X4703 = X4704
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X4702,X4704),X4703)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_nat__less__cases])])]) ).

fof(i_0_2313,plain,
    ! [X4707,X4708,X4709] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4707),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4708),X4709)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4708),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4707),X4709)),
    inference(variable_rename,[status(thm)],[fact_223_nat__add__left__commute]) ).

cnf(i_0_2314,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_1304]) ).

cnf(i_0_2315,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_1336]) ).

cnf(i_0_2316,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_1337]) ).

cnf(i_0_2317,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_1338]) ).

cnf(i_0_2318,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_1339]) ).

cnf(i_0_2319,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_1340]) ).

cnf(i_0_2320,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_1341]) ).

cnf(i_0_2321,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_1342]) ).

cnf(i_0_2322,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_1343]) ).

cnf(i_0_2323,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_1344]) ).

cnf(i_0_2324,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_1345]) ).

cnf(i_0_2325,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_1344]) ).

fof(i_0_2326,plain,
    ! [X5123,X5124,X5126] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk82_2(X5123,X5124)),X5123))
        | ~ hBOOL(hAPP(nat,bool,X5124,X5123))
        | hBOOL(hAPP(nat,bool,X5124,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5126),esk82_2(X5123,X5124)))
        | ~ hBOOL(hAPP(nat,bool,X5124,X5126))
        | ~ hBOOL(hAPP(nat,bool,X5124,X5123))
        | hBOOL(hAPP(nat,bool,X5124,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X5124,esk82_2(X5123,X5124)))
        | ~ hBOOL(hAPP(nat,bool,X5124,X5123))
        | hBOOL(hAPP(nat,bool,X5124,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_1346])])])])]) ).

fof(i_0_2327,plain,
    ! [X4666,X4667,X4668,X4669] :
      ( ~ hBOOL(hAPP(fun(X4666,bool),bool,hAPP(fun(X4666,bool),fun(fun(X4666,bool),bool),ord_less_eq(fun(X4666,bool)),X4668),X4669))
      | ~ hBOOL(hAPP(X4666,bool,X4668,X4667))
      | hBOOL(hAPP(X4666,bool,X4669,X4667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_207_predicate1D])]) ).

fof(i_0_2328,plain,
    ! [X4680,X4681,X4682,X4683] :
      ( ~ hBOOL(hAPP(X4680,bool,X4682,X4683))
      | ~ hBOOL(hAPP(fun(X4680,bool),bool,hAPP(fun(X4680,bool),fun(fun(X4680,bool),bool),ord_less_eq(fun(X4680,bool)),X4682),X4681))
      | hBOOL(hAPP(X4680,bool,X4681,X4683)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_rev__predicate1D])]) ).

fof(i_0_2329,plain,
    ! [X4937,X4938] :
      ( hBOOL(hAPP(fun(X4937,bool),bool,finite_finite_1(X4937),top_top(fun(X4937,bool))))
      | ~ hBOOL(hAPP(fun(X4937,bool),bool,finite_finite_1(X4937),X4938))
      | ~ hBOOL(hAPP(fun(X4937,bool),bool,hAPP(X4937,fun(fun(X4937,bool),bool),member(X4937),esk70_2(X4937,X4938)),X4938)) ),
    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_1347])])])])]) ).

cnf(i_0_2330,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),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1332]) ).

cnf(i_0_2331,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_1348]) ).

cnf(i_0_2332,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X1,X2)),arrow_1568854078le_Lin))
    | ti(arrow_2142409994le_alt,X1) = ti(arrow_2142409994le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1259]) ).

fof(i_0_2333,plain,
    ! [X5212,X5213,X5215,X5216,X5217] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5212),X5213))
        | X5213 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5212),esk86_2(X5212,X5213))) )
      & ( X5216 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5215),X5217))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5215),X5216)) ) ),
    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_less__iff__Suc__add])])])])]) ).

cnf(i_0_2334,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_1302]) ).

fof(i_0_2335,plain,
    ! [X7611,X7612,X7613,X7614,X7615,X7616] : hAPP(X7611,X7612,hAPP(fun(X7611,X7613),fun(X7611,X7612),hAPP(fun(X7611,fun(X7613,X7612)),fun(fun(X7611,X7613),fun(X7611,X7612)),combs(X7611,X7613,X7612),X7614),X7615),X7616) = hAPP(X7613,X7612,hAPP(X7611,fun(X7613,X7612),X7614,X7616),hAPP(X7611,X7613,X7615,X7616)),
    inference(variable_rename,[status(thm)],[help_COMBS_1_1_U]) ).

cnf(i_0_2336,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk77_4(X2,X1,X3,X4)) != ti(X1,esk78_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1349]) ).

cnf(i_0_2337,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk31_4(X1,X2,X3,X4)) != ti(X1,esk32_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1263]) ).

cnf(i_0_2338,plain,
    ti(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1350]) ).

fof(i_0_2339,plain,
    ! [X5271,X5272] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5271),esk94_2(X5271,X5272)))
        | X5272 = hAPP(nat,nat,suc,X5271)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5271),X5272)) )
      & ( X5272 = hAPP(nat,nat,suc,esk94_2(X5271,X5272))
        | X5272 = hAPP(nat,nat,suc,X5271)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5271),X5272)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_439_lessE])])])]) ).

fof(i_0_2340,plain,
    ! [X5246,X5247] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5246),X5247))
      | X5247 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5246),esk88_2(X5246,X5247))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_less__imp__Suc__add])])]) ).

fof(i_0_2341,plain,
    ! [X4292,X4293,X4294] :
      ( ~ preorder(X4292)
      | ~ hBOOL(hAPP(X4292,bool,hAPP(X4292,fun(X4292,bool),ord_less(X4292),X4293),X4294))
      | hBOOL(hAPP(X4292,bool,hAPP(X4292,fun(X4292,bool),ord_less_eq(X4292),X4293),X4294)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_123_order__less__imp__le])])]) ).

cnf(i_0_2342,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_1348]) ).

cnf(i_0_2343,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),arrow_708804735ctator) = arrow_708804735ctator,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Odictator_res]) ).

fof(i_0_2344,plain,
    ! [X6164,X6165] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X6164)),X6165) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6165),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6164),X6165)),
    inference(variable_rename,[status(thm)],[fact_667_mult__Suc]) ).

fof(i_0_2345,plain,
    ! [X5743,X5744] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X5743),X5744))),
    inference(variable_rename,[status(thm)],[fact_549_finite__greaterThanLessThan]) ).

fof(i_0_2346,plain,
    ! [X5741,X5742] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X5741),X5742))),
    inference(variable_rename,[status(thm)],[fact_548_finite__greaterThanAtMost]) ).

fof(i_0_2347,plain,
    ! [X5336,X5337] : 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),X5336),X5337))),
    inference(variable_rename,[status(thm)],[fact_460_finite__atLeastLessThan]) ).

fof(i_0_2348,plain,
    ! [X6617,X6618] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X6617),X6618))),
    inference(variable_rename,[status(thm)],[fact_761_finite__atLeastAtMost]) ).

fof(i_0_2349,plain,
    ! [X5127,X5128] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk83_2(X5127,X5128)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5127),X5128)) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5127),esk83_2(X5127,X5128)) = X5128
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5127),X5128)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_370_less__imp__add__positive])])])]) ).

fof(i_0_2350,plain,
    ! [X4011,X4012,X4013,X4014,X4015,X4016] : hAPP(product_prod(X4011,X4012),X4013,hAPP(fun(X4011,fun(X4012,X4013)),fun(product_prod(X4011,X4012),X4013),product_prod_rec(X4011,X4012,X4013),X4014),hAPP(X4012,product_prod(X4011,X4012),hAPP(X4011,fun(X4012,product_prod(X4011,X4012)),product_Pair(X4011,X4012),X4015),X4016)) = hAPP(X4012,X4013,hAPP(X4011,fun(X4012,X4013),X4014,X4015),X4016),
    inference(variable_rename,[status(thm)],[fact_28_prod_Orecs]) ).

fof(i_0_2351,plain,
    ! [X4764,X4765] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4764),X4765))
      | X4764 = X4765
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4764),X4765)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_le__neq__implies__less])]) ).

fof(i_0_2352,plain,
    ! [X4760,X4761] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4760),X4761))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4760),X4761))
        | X4760 = X4761 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4760),X4761))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4760),X4761)) )
      & ( X4760 != X4761
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4760),X4761)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_243_le__eq__less__or__eq])])]) ).

fof(i_0_2353,plain,
    ! [X4758,X4759] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4758),X4759))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4758),X4759)) )
      & ( X4758 != X4759
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4758),X4759)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4758),X4759))
        | X4758 = X4759
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4758),X4759)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_242_nat__less__le])])]) ).

fof(i_0_2354,plain,
    ! [X4832,X4833] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4832),X4833))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4832),X4833)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_termination__basic__simps_I5_J])]) ).

fof(i_0_2355,plain,
    ! [X4766,X4767] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4766),X4767))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4766),X4767)) )
      & ( X4766 != X4767
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4766),X4767)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_less__or__eq__imp__le])])]) ).

fof(i_0_2356,plain,
    ! [X4762,X4763] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4762),X4763))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4762),X4763)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_less__imp__le__nat])]) ).

fof(i_0_2357,plain,
    ! [X5197] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5197),hAPP(nat,nat,suc,zero_zero(nat))))
        | X5197 = zero_zero(nat) )
      & ( X5197 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5197),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_409_less__Suc0])]) ).

cnf(i_0_2358,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_1336]) ).

cnf(i_0_2359,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1066301521nimity) = arrow_1066301521nimity,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Ounanimity_res]) ).

cnf(i_0_2360,plain,
    ti(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OIIA_res]) ).

fof(i_0_2361,plain,
    ! [X5115] :
      ( ~ hBOOL(hAPP(fun(X5115,bool),bool,finite_finite_1(X5115),top_top(fun(X5115,bool))))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X5115,bool),nat,finite_card(X5115),top_top(fun(X5115,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_366_finite__UNIV__card__ge__0])]) ).

fof(i_0_2362,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk66_0),arrow_1568854078le_Lin)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_271_linear__alt])]) ).

fof(i_0_2363,plain,
    ! [X5284,X5285] :
      ( ( hBOOL(hAPP(nat,bool,X5285,esk99_2(X5284,X5285)))
        | hBOOL(hAPP(nat,bool,X5285,X5284))
        | ~ hBOOL(hAPP(nat,bool,X5285,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,X5285,hAPP(nat,nat,suc,esk99_2(X5284,X5285))))
        | hBOOL(hAPP(nat,bool,X5285,X5284))
        | ~ hBOOL(hAPP(nat,bool,X5285,zero_zero(nat))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_444_nat__induct])])])]) ).

cnf(i_0_2364,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_1351]) ).

cnf(i_0_2365,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_1352]) ).

cnf(i_0_2366,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_1353]) ).

cnf(i_0_2367,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_1354]) ).

cnf(i_0_2368,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_1328]) ).

cnf(i_0_2369,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_1355]) ).

cnf(i_0_2370,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_1356]) ).

fof(i_0_2371,plain,
    ! [X6434,X6435,X6436,X6437,X6438,X6439] : hAPP(X6434,X6435,hAPP(fun(X6434,X6436),fun(X6434,X6435),hAPP(fun(X6436,X6435),fun(fun(X6434,X6436),fun(X6434,X6435)),comp(X6436,X6435,X6434),X6437),X6438),X6439) = hAPP(X6436,X6435,X6437,hAPP(X6434,X6436,X6438,X6439)),
    inference(variable_rename,[status(thm)],[fact_730_o__apply]) ).

fof(i_0_2372,plain,
    ! [X6421,X6422,X6423,X6424,X6425,X6426] : hAPP(X6421,X6422,hAPP(fun(X6421,X6423),fun(X6421,X6422),hAPP(fun(X6423,X6422),fun(fun(X6421,X6423),fun(X6421,X6422)),comp(X6423,X6422,X6421),X6424),X6425),X6426) = hAPP(X6423,X6422,X6424,hAPP(X6421,X6423,X6425,X6426)),
    inference(variable_rename,[status(thm)],[fact_728_o__def]) ).

fof(i_0_2373,plain,
    ! [X7593,X7594,X7595,X7596,X7597,X7598] : hAPP(X7593,X7594,hAPP(fun(X7593,X7595),fun(X7593,X7594),hAPP(fun(X7595,X7594),fun(fun(X7593,X7595),fun(X7593,X7594)),combb(X7595,X7594,X7593),X7596),X7597),X7598) = hAPP(X7595,X7594,X7596,hAPP(X7593,X7595,X7597,X7598)),
    inference(variable_rename,[status(thm)],[help_COMBB_1_1_U]) ).

fof(i_0_2374,plain,
    ! [X7599,X7600,X7601,X7602,X7603,X7604] : hAPP(X7599,X7600,hAPP(X7601,fun(X7599,X7600),hAPP(fun(X7599,fun(X7601,X7600)),fun(X7601,fun(X7599,X7600)),combc(X7599,X7601,X7600),X7602),X7603),X7604) = hAPP(X7601,X7600,hAPP(X7599,fun(X7601,X7600),X7602,X7604),X7603),
    inference(variable_rename,[status(thm)],[help_COMBC_1_1_U]) ).

cnf(i_0_2375,plain,
    ( hAPP(X2,X3,X4,hAPP(X1,X2,X5,X7)) = hAPP(X1,X3,X6,X7)
    | hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),X5) != ti(fun(X1,X3),X6) ),
    inference(split_conjunct,[status(thm)],[i_0_1357]) ).

fof(i_0_2376,plain,
    ! [X6162,X6163] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6162),hAPP(nat,nat,suc,X6163)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X6162),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6162),X6163)),
    inference(variable_rename,[status(thm)],[fact_666_mult__Suc__right]) ).

cnf(i_0_2377,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1358]) ).

cnf(i_0_2378,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1359]) ).

cnf(i_0_2379,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2) = ti(X1,X3)
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1360]) ).

cnf(i_0_2380,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

cnf(i_0_2381,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = ti(X1,X2)
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1362]) ).

cnf(i_0_2382,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) = ti(X1,X2)
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1363]) ).

cnf(i_0_2383,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_1364]) ).

cnf(i_0_2384,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_1365]) ).

cnf(i_0_2385,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_1364]) ).

cnf(i_0_2386,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_1365]) ).

fof(i_0_2387,plain,
    ! [X5175,X5176] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X5175)),X5176) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5175),X5176)),
    inference(variable_rename,[status(thm)],[fact_398_add__Suc]) ).

cnf(i_0_2388,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_1364]) ).

cnf(i_0_2389,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1665824030_below) = arrow_1665824030_below,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Obelow_res]) ).

cnf(i_0_2390,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_357225482_above) = arrow_357225482_above,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Oabove_res]) ).

cnf(i_0_2391,plain,
    ( top_top(fun(X1,bool)) = ti(fun(X1,bool),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk149_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1366]) ).

cnf(i_0_2392,plain,
    ti(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),compose(X1,X2,X3)) = compose(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

fof(i_0_2393,plain,
    ! [X4126,X4127,X4128] :
      ( ( ~ hBOOL(hAPP(fun(X4126,bool),bool,hAPP(X4126,fun(fun(X4126,bool),bool),member(X4126),X4127),X4128))
        | hBOOL(hAPP(X4126,bool,X4128,X4127)) )
      & ( ~ hBOOL(hAPP(X4126,bool,X4128,X4127))
        | hBOOL(hAPP(fun(X4126,bool),bool,hAPP(X4126,fun(fun(X4126,bool),bool),member(X4126),X4127),X4128)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_mem__def])]) ).

cnf(i_0_2394,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_1352]) ).

cnf(i_0_2395,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_1352]) ).

cnf(i_0_2396,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_1353]) ).

cnf(i_0_2397,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_1342]) ).

cnf(i_0_2398,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_1368]) ).

cnf(i_0_2399,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_1369]) ).

cnf(i_0_2400,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_1370]) ).

cnf(i_0_2401,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != ti(X1,X3)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1359]) ).

cnf(i_0_2402,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != ti(X1,X2)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

fof(i_0_2403,plain,
    ! [X4772,X4773,X4775,X4776,X4777] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4772),X4773))
        | X4773 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4772),esk56_2(X4772,X4773)) )
      & ( X4776 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4775),X4777)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4775),X4776)) ) ),
    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_249_le__iff__add])])])])]) ).

cnf(i_0_2404,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_1371]) ).

fof(i_0_2405,plain,
    ! [X6889,X6890,X6891] :
      ( ~ lattice(X6889)
      | hAPP(X6889,X6889,hAPP(X6889,fun(X6889,X6889),semilattice_sup_sup(X6889),X6890),hAPP(X6889,X6889,hAPP(X6889,fun(X6889,X6889),semilattice_sup_sup(X6889),X6890),X6891)) = hAPP(X6889,X6889,hAPP(X6889,fun(X6889,X6889),semilattice_sup_sup(X6889),X6890),X6891) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_828_inf__sup__aci_I8_J])])]) ).

fof(i_0_2406,plain,
    ! [X6892,X6893,X6894] :
      ( ~ semilattice_sup(X6892)
      | hAPP(X6892,X6892,hAPP(X6892,fun(X6892,X6892),semilattice_sup_sup(X6892),X6893),hAPP(X6892,X6892,hAPP(X6892,fun(X6892,X6892),semilattice_sup_sup(X6892),X6893),X6894)) = hAPP(X6892,X6892,hAPP(X6892,fun(X6892,X6892),semilattice_sup_sup(X6892),X6893),X6894) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_829_sup__left__idem])])]) ).

fof(i_0_2407,plain,
    ! [X6886,X6887,X6888] :
      ( ~ semilattice_sup(X6886)
      | hAPP(X6886,X6886,hAPP(X6886,fun(X6886,X6886),semilattice_sup_sup(X6886),X6887),hAPP(X6886,X6886,hAPP(X6886,fun(X6886,X6886),semilattice_sup_sup(X6886),X6887),X6888)) = hAPP(X6886,X6886,hAPP(X6886,fun(X6886,X6886),semilattice_sup_sup(X6886),X6887),X6888) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_827_sup_Oleft__idem])])]) ).

fof(i_0_2408,plain,
    ! [X7328,X7329,X7330] :
      ( ~ lattice(X7328)
      | hAPP(X7328,X7328,hAPP(X7328,fun(X7328,X7328),semilattice_inf_inf(X7328),X7329),hAPP(X7328,X7328,hAPP(X7328,fun(X7328,X7328),semilattice_inf_inf(X7328),X7329),X7330)) = hAPP(X7328,X7328,hAPP(X7328,fun(X7328,X7328),semilattice_inf_inf(X7328),X7329),X7330) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_945_inf__sup__aci_I4_J])])]) ).

fof(i_0_2409,plain,
    ! [X7331,X7332,X7333] :
      ( ~ semilattice_inf(X7331)
      | hAPP(X7331,X7331,hAPP(X7331,fun(X7331,X7331),semilattice_inf_inf(X7331),X7332),hAPP(X7331,X7331,hAPP(X7331,fun(X7331,X7331),semilattice_inf_inf(X7331),X7332),X7333)) = hAPP(X7331,X7331,hAPP(X7331,fun(X7331,X7331),semilattice_inf_inf(X7331),X7332),X7333) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_946_inf_Oleft__idem])])]) ).

fof(i_0_2410,plain,
    ! [X7325,X7326,X7327] :
      ( ~ semilattice_inf(X7325)
      | hAPP(X7325,X7325,hAPP(X7325,fun(X7325,X7325),semilattice_inf_inf(X7325),X7326),hAPP(X7325,X7325,hAPP(X7325,fun(X7325,X7325),semilattice_inf_inf(X7325),X7326),X7327)) = hAPP(X7325,X7325,hAPP(X7325,fun(X7325,X7325),semilattice_inf_inf(X7325),X7326),X7327) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_944_inf__left__idem])])]) ).

fof(i_0_2411,plain,
    ! [X6870,X6871,X6872] :
      ( ~ ab_sem1668676832m_mult(X6870)
      | hAPP(X6870,X6870,hAPP(X6870,fun(X6870,X6870),times_times(X6870),X6871),hAPP(X6870,X6870,hAPP(X6870,fun(X6870,X6870),times_times(X6870),X6871),X6872)) = hAPP(X6870,X6870,hAPP(X6870,fun(X6870,X6870),times_times(X6870),X6871),X6872) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_821_mult__left__idem])])]) ).

fof(i_0_2412,plain,
    ! [X6369,X6370,X6371] :
      ( ( hBOOL(hAPP(X6369,bool,X6371,esk151_3(X6369,X6370,X6371)))
        | hBOOL(hAPP(fun(X6369,bool),bool,hAPP(fun(X6369,bool),fun(fun(X6369,bool),bool),ord_less_eq(fun(X6369,bool)),X6371),X6370)) )
      & ( ~ hBOOL(hAPP(X6369,bool,X6370,esk151_3(X6369,X6370,X6371)))
        | hBOOL(hAPP(fun(X6369,bool),bool,hAPP(fun(X6369,bool),fun(fun(X6369,bool),bool),ord_less_eq(fun(X6369,bool)),X6371),X6370)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_717_predicate1I])])])]) ).

fof(i_0_2413,plain,
    ! [X4245,X4246,X4247] :
      ( ~ linorder(X4245)
      | hBOOL(hAPP(X4245,bool,hAPP(X4245,fun(X4245,bool),ord_less_eq(X4245),X4246),X4247))
      | hBOOL(hAPP(X4245,bool,hAPP(X4245,fun(X4245,bool),ord_less_eq(X4245),X4247),X4246)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_109_linorder__linear])])]) ).

fof(i_0_2414,plain,
    ! [X4193,X4194,X4195] :
      ( ~ linorder(X4193)
      | hBOOL(hAPP(X4193,bool,hAPP(X4193,fun(X4193,bool),ord_less_eq(X4193),X4194),X4195))
      | hBOOL(hAPP(X4193,bool,hAPP(X4193,fun(X4193,bool),ord_less_eq(X4193),X4195),X4194)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1372])])]) ).

fof(i_0_2415,plain,
    ! [X4274,X4275,X4276] :
      ( ~ linorder(X4274)
      | hBOOL(hAPP(X4274,bool,hAPP(X4274,fun(X4274,bool),ord_less(X4274),X4275),X4276))
      | hBOOL(hAPP(X4274,bool,hAPP(X4274,fun(X4274,bool),ord_less_eq(X4274),X4276),X4275)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1373])])]) ).

fof(i_0_2416,plain,
    ! [X4277,X4278,X4279] :
      ( ~ linorder(X4277)
      | hBOOL(hAPP(X4277,bool,hAPP(X4277,fun(X4277,bool),ord_less_eq(X4277),X4278),X4279))
      | hBOOL(hAPP(X4277,bool,hAPP(X4277,fun(X4277,bool),ord_less(X4277),X4279),X4278)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1374])])]) ).

fof(i_0_2417,plain,
    ! [X4262,X4263,X4264] :
      ( ~ linorder(X4262)
      | hBOOL(hAPP(X4262,bool,hAPP(X4262,fun(X4262,bool),ord_less_eq(X4262),X4263),X4264))
      | hBOOL(hAPP(X4262,bool,hAPP(X4262,fun(X4262,bool),ord_less(X4262),X4264),X4263)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_linorder__le__less__linear])])]) ).

cnf(i_0_2418,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_1293]) ).

cnf(i_0_2419,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_1293]) ).

cnf(i_0_2420,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_1375]) ).

cnf(i_0_2421,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_1376]) ).

cnf(i_0_2422,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_1376]) ).

cnf(i_0_2423,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_1301]) ).

cnf(i_0_2424,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_1377]) ).

cnf(i_0_2425,plain,
    ti(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1378]) ).

fof(i_0_2426,plain,
    ! [X5000,X5001] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X5000,X5001)),X5001))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X5001)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X5000,X5001)),X5000))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X5001)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_315_bounded__nat__set__is__finite])])])]) ).

cnf(i_0_2427,plain,
    ti(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),mlex_prod(X1)) = mlex_prod(X1),
    inference(split_conjunct,[status(thm)],[i_0_1379]) ).

fof(i_0_2428,plain,
    ! [X4924,X4925] :
      ( ( hBOOL(hAPP(fun(X4924,bool),bool,finite_finite_1(X4924),top_top(fun(X4924,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X4924,X4925),bool),bool,finite_finite_1(sum_sum(X4924,X4925)),top_top(fun(sum_sum(X4924,X4925),bool)))) )
      & ( hBOOL(hAPP(fun(X4925,bool),bool,finite_finite_1(X4925),top_top(fun(X4925,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X4924,X4925),bool),bool,finite_finite_1(sum_sum(X4924,X4925)),top_top(fun(sum_sum(X4924,X4925),bool)))) )
      & ( ~ hBOOL(hAPP(fun(X4924,bool),bool,finite_finite_1(X4924),top_top(fun(X4924,bool))))
        | ~ hBOOL(hAPP(fun(X4925,bool),bool,finite_finite_1(X4925),top_top(fun(X4925,bool))))
        | hBOOL(hAPP(fun(sum_sum(X4924,X4925),bool),bool,finite_finite_1(sum_sum(X4924,X4925)),top_top(fun(sum_sum(X4924,X4925),bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_295_finite__Plus__UNIV__iff])])]) ).

fof(i_0_2429,plain,
    ! [X4926,X4927] :
      ( ~ hBOOL(hAPP(fun(X4927,bool),bool,finite_finite_1(X4927),top_top(fun(X4927,bool))))
      | ~ hBOOL(hAPP(fun(X4926,bool),bool,finite_finite_1(X4926),top_top(fun(X4926,bool))))
      | hBOOL(hAPP(fun(product_prod(X4927,X4926),bool),bool,finite_finite_1(product_prod(X4927,X4926)),top_top(fun(product_prod(X4927,X4926),bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_296_finite__Prod__UNIV])]) ).

cnf(i_0_2430,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_1380]) ).

fof(i_0_2431,plain,
    ! [X4695,X4696] :
      ( X4695 = X4696
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4695),X4696))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4696),X4695)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1381])]) ).

fof(i_0_2432,plain,
    ! [X4693,X4694] :
      ( ( X4693 = X4694
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4693),X4694))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4694),X4693)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4693),X4694))
        | X4693 != X4694 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4694),X4693))
        | X4693 != X4694 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_nat__neq__iff])])]) ).

fof(i_0_2433,plain,
    ! [X4720,X4721] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4720),X4721))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4721),X4720)) ),
    inference(variable_rename,[status(thm)],[fact_228_nat__le__linear]) ).

fof(i_0_2434,plain,
    ! [X5120,X5121] :
      ( ( hBOOL(hAPP(fun(X5120,bool),bool,hAPP(X5120,fun(fun(X5120,bool),bool),member(X5120),esk81_2(X5120,X5121)),X5121))
        | hAPP(fun(X5120,bool),nat,finite_card(X5120),X5121) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X5120,bool),bool,finite_finite_1(X5120),X5121)) )
      & ( one_one(nat) != zero_zero(nat)
        | hAPP(fun(X5120,bool),nat,finite_card(X5120),X5121) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X5120,bool),bool,finite_finite_1(X5120),X5121)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_368_card_Oneutral])])])]) ).

fof(i_0_2435,plain,
    ! [X5177,X5178] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5177),hAPP(nat,nat,suc,X5178)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5177),X5178)),
    inference(variable_rename,[status(thm)],[fact_399_add__Suc__right]) ).

cnf(i_0_2436,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_1382]) ).

cnf(i_0_2437,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_1383]) ).

cnf(i_0_2438,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_1384]) ).

cnf(i_0_2439,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_1385]) ).

cnf(i_0_2440,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_1386]) ).

cnf(i_0_2441,plain,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk21_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1387]) ).

fof(i_0_2442,plain,
    ! [X5709,X5710,X5711,X5712] : hAPP(nat,X5709,hAPP(fun(nat,X5709),fun(nat,X5709),hAPP(X5709,fun(fun(nat,X5709),fun(nat,X5709)),nat_case(X5709),X5710),X5711),hAPP(nat,nat,suc,X5712)) = hAPP(nat,X5709,X5711,X5712),
    inference(variable_rename,[status(thm)],[fact_540_nat__case__Suc]) ).

cnf(i_0_2443,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_1388]) ).

fof(i_0_2444,plain,
    ! [X5173,X5174] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X5173)),X5174) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5173),hAPP(nat,nat,suc,X5174)),
    inference(variable_rename,[status(thm)],[fact_397_add__Suc__shift]) ).

fof(i_0_2445,plain,
    ! [X6509] : hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X6509)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X6509)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(variable_rename,[status(thm)],[fact_740_nat_Osize_I4_J]) ).

fof(i_0_2446,plain,
    ! [X6380] : hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X6380)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X6380)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(variable_rename,[status(thm)],[fact_719_nat_Osize_I2_J]) ).

cnf(i_0_2447,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_1389]) ).

fof(i_0_2448,plain,
    ! [X5132,X5133] :
      ( ~ hBOOL(hAPP(fun(fun(X5132,X5133),bool),bool,finite_finite_1(fun(X5132,X5133)),top_top(fun(fun(X5132,X5133),bool))))
      | hAPP(fun(X5133,bool),nat,finite_card(X5133),top_top(fun(X5133,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
      | hBOOL(hAPP(fun(X5132,bool),bool,finite_finite_1(X5132),top_top(fun(X5132,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_372_finite__fun__UNIVD1])]) ).

cnf(i_0_2449,plain,
    ( ti(X2,X4) = hAPP(X1,X2,X3,esk129_4(X1,X2,X3,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_1390]) ).

cnf(i_0_2450,plain,
    ( ti(X2,X4) = hAPP(X1,X2,X3,esk127_4(X1,X2,X4,X3))
    | 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_1391]) ).

cnf(i_0_2451,plain,
    ( ti(X2,X4) = hAPP(X1,X2,X3,esk126_4(X1,X2,X4,X3))
    | 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_1392]) ).

cnf(i_0_2452,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_1393]) ).

cnf(i_0_2453,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_1394]) ).

fof(i_0_2454,plain,
    ! [X5281,X5282] :
      ( ( hBOOL(hAPP(nat,bool,X5281,hAPP(nat,nat,suc,esk98_1(X5281))))
        | hBOOL(hAPP(nat,bool,X5281,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X5281,X5282)) )
      & ( ~ hBOOL(hAPP(nat,bool,X5281,esk98_1(X5281)))
        | hBOOL(hAPP(nat,bool,X5281,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X5281,X5282)) ) ),
    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_443_zero__induct])])])])])]) ).

fof(i_0_2455,plain,
    ! [X5764,X5765] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X5764)),X5765) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X5764),X5765),
    inference(variable_rename,[status(thm)],[fact_554_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_2456,plain,
    ! [X6644,X6645] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X6644)),X6645) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X6644),X6645),
    inference(variable_rename,[status(thm)],[fact_767_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_2457,plain,
    ! [X5249] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5249))
      | X5249 = hAPP(nat,nat,suc,esk89_1(X5249)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_gr0__implies__Suc])])]) ).

fof(i_0_2458,plain,
    ! [X5193,X5195,X5196] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5193))
        | X5193 = hAPP(nat,nat,suc,esk84_1(X5193)) )
      & ( X5195 != hAPP(nat,nat,suc,X5196)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5195)) ) ),
    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_408_gr0__conv__Suc])])])])]) ).

cnf(i_0_2459,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = ti(X1,X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1395]) ).

cnf(i_0_2460,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = ti(X1,X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1396]) ).

fof(i_0_2461,plain,
    ( hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))))
    & hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_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_2462,plain,
    ! [X4175,X4176,X4177] : hAPP(fun(X4175,fun(X4176,bool)),fun(fun(X4175,X4176),bool),hAPP(fun(X4175,bool),fun(fun(X4175,fun(X4176,bool)),fun(fun(X4175,X4176),bool)),pi(X4175,X4176),X4177),hAPP(fun(X4176,bool),fun(X4175,fun(X4176,bool)),combk(fun(X4176,bool),X4175),top_top(fun(X4176,bool)))) = top_top(fun(fun(X4175,X4176),bool)),
    inference(variable_rename,[status(thm)],[fact_89_Pi__UNIV]) ).

fof(i_0_2463,plain,
    ! [X5085] :
      ( ~ linordered_semidom(X5085)
      | ~ hBOOL(hAPP(X5085,bool,hAPP(X5085,fun(X5085,bool),ord_less_eq(X5085),one_one(X5085)),zero_zero(X5085))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1397])]) ).

fof(i_0_2464,plain,
    ! [X5087] :
      ( ~ linordered_semidom(X5087)
      | ~ hBOOL(hAPP(X5087,bool,hAPP(X5087,fun(X5087,bool),ord_less(X5087),one_one(X5087)),zero_zero(X5087))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1398])]) ).

cnf(i_0_2465,plain,
    hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1399]) ).

fof(i_0_2466,plain,
    ! [X4020,X4021] :
      ( ~ top(X4020)
      | ~ hBOOL(hAPP(X4020,bool,hAPP(X4020,fun(X4020,bool),ord_less(X4020),top_top(X4020)),X4021)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1400])])]) ).

fof(i_0_2467,plain,
    ! [X5137] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X5137))),
    inference(variable_rename,[status(thm)],[fact_375_zero__less__Suc]) ).

fof(i_0_2468,plain,
    ! [X5134] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5134),hAPP(nat,nat,suc,X5134))),
    inference(variable_rename,[status(thm)],[fact_373_lessI]) ).

fof(i_0_2469,plain,
    ! [X4119,X4120] :
      ( ~ preorder(X4119)
      | ~ hBOOL(hAPP(X4119,bool,hAPP(X4119,fun(X4119,bool),ord_less(X4119),X4120),X4120)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1401])])]) ).

fof(i_0_2470,plain,
    ! [X5036] :
      ( ( X5036 = zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5036)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5036))
        | X5036 != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_330_neq0__conv])]) ).

fof(i_0_2471,plain,
    ! [X5047] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5047),zero_zero(nat)))
        | X5047 = zero_zero(nat) )
      & ( X5047 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5047),zero_zero(nat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_338_le__0__eq])]) ).

fof(i_0_2472,plain,
    ! [X5037] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5037),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_1402]) ).

fof(i_0_2473,plain,
    ! [X5035] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5035),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_1403]) ).

fof(i_0_2474,plain,
    ! [X5019] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5019),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[i_0_1404]) ).

fof(i_0_2475,plain,
    ! [X5038,X5039] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5038),X5039))
      | X5039 != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_332_gr__implies__not0])]) ).

fof(i_0_2476,plain,
    ! [X4700,X4701] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4700),X4701))
      | X4700 != X4701 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_220_less__not__refl3])]) ).

fof(i_0_2477,plain,
    ! [X4698,X4699] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4698),X4699))
      | X4699 != X4698 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_219_less__not__refl2])]) ).

fof(i_0_2478,plain,
    ! [X5973,X5974,X5975] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5973),X5974) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5975),X5974)
        | X5973 = X5975
        | X5974 = zero_zero(nat) )
      & ( X5973 != X5975
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5973),X5974) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5975),X5974) )
      & ( X5974 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5973),X5974) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5975),X5974) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_607_mult__cancel2])])]) ).

fof(i_0_2479,plain,
    ! [X6310,X6311,X6312] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6311) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6312)
        | X6310 = zero_zero(nat)
        | X6311 = X6312 )
      & ( X6310 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6311) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6312) )
      & ( X6311 != X6312
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6311) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6310),X6312) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_707_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_2480,plain,
    ! [X5976,X5977,X5978] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5977) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5978)
        | X5977 = X5978
        | X5976 = zero_zero(nat) )
      & ( X5977 != X5978
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5977) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5978) )
      & ( X5976 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5977) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5976),X5978) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_608_mult__cancel1])])]) ).

fof(i_0_2481,plain,
    ! [X4697] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4697),X4697)),
    inference(variable_rename,[status(thm)],[i_0_1405]) ).

fof(i_0_2482,plain,
    ! [X4692] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4692),X4692)),
    inference(variable_rename,[status(thm)],[i_0_1406]) ).

fof(i_0_2483,plain,
    ! [X4716,X4717,X4718] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4716),X4717) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4718),X4717)
        | X4716 = X4718 )
      & ( X4716 != X4718
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4716),X4717) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4718),X4717) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_226_nat__add__right__cancel])]) ).

fof(i_0_2484,plain,
    ! [X4713,X4714,X4715] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4713),X4714) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4713),X4715)
        | X4714 = X4715 )
      & ( X4714 != X4715
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4713),X4714) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4713),X4715) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_nat__add__left__cancel])]) ).

fof(i_0_2485,plain,
    ! [X7518,X7519] : hAPP(fun(X7518,bool),nat,finite_card(X7518),X7519) = hAPP(fun(X7518,bool),nat,hAPP(fun(X7518,nat),fun(fun(X7518,bool),nat),big_co1399186613setsum(X7518,nat),hAPP(nat,fun(X7518,nat),combk(nat,X7518),one_one(nat))),X7519),
    inference(variable_rename,[status(thm)],[fact_990_card__eq__setsum]) ).

fof(i_0_2486,plain,
    ! [X7628,X7629] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X7628),X7629))
      | hBOOL(X7628)
      | hBOOL(X7629) ),
    inference(variable_rename,[status(thm)],[i_0_1407]) ).

fof(i_0_2487,plain,
    ! [X7620,X7621] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X7620),X7621))
      | hBOOL(X7620) ),
    inference(variable_rename,[status(thm)],[i_0_1408]) ).

fof(i_0_2488,plain,
    ! [X7622,X7623] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X7622),X7623))
      | hBOOL(X7623) ),
    inference(variable_rename,[status(thm)],[i_0_1409]) ).

cnf(i_0_2489,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_1382]) ).

cnf(i_0_2490,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_1385]) ).

cnf(i_0_2491,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_1341]) ).

cnf(i_0_2492,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_1310]) ).

cnf(i_0_2493,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_1310]) ).

cnf(i_0_2494,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_1410]) ).

cnf(i_0_2495,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_1411]) ).

cnf(i_0_2496,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_1412]) ).

cnf(i_0_2497,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_1413]) ).

cnf(i_0_2498,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_1414]) ).

fof(i_0_2499,plain,
    ! [X6741,X6742,X6743] : hAPP(fun(X6741,bool),fun(X6741,bool),hAPP(fun(X6741,bool),fun(fun(X6741,bool),fun(X6741,bool)),semilattice_sup_sup(fun(X6741,bool)),X6742),X6743) = hAPP(fun(X6741,bool),fun(X6741,bool),hAPP(fun(X6741,bool),fun(fun(X6741,bool),fun(X6741,bool)),semilattice_sup_sup(fun(X6741,bool)),X6743),X6742),
    inference(variable_rename,[status(thm)],[fact_793_Un__commute]) ).

fof(i_0_2500,plain,
    ! [X7186,X7187,X7188] : hAPP(fun(X7186,bool),fun(X7186,bool),hAPP(fun(X7186,bool),fun(fun(X7186,bool),fun(X7186,bool)),semilattice_inf_inf(fun(X7186,bool)),X7187),X7188) = hAPP(fun(X7186,bool),fun(X7186,bool),hAPP(fun(X7186,bool),fun(fun(X7186,bool),fun(X7186,bool)),semilattice_inf_inf(fun(X7186,bool)),X7188),X7187),
    inference(variable_rename,[status(thm)],[fact_906_Int__commute]) ).

fof(i_0_2501,plain,
    ! [X4933,X4934] :
      ( ~ hBOOL(hAPP(fun(fun(X4933,X4934),bool),bool,finite_finite_1(fun(X4933,X4934)),top_top(fun(fun(X4933,X4934),bool))))
      | hBOOL(hAPP(fun(X4934,bool),bool,finite_finite_1(X4934),top_top(fun(X4934,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_300_finite__fun__UNIVD2])]) ).

fof(i_0_2502,plain,
    ! [X6624,X6625] : hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X6624),hAPP(nat,nat,suc,X6625)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X6624),X6625),
    inference(variable_rename,[status(thm)],[fact_763_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_2503,plain,
    ! [X7465,X7466,X7467] :
      ( ~ comm_monoid_add(X7466)
      | hAPP(fun(X7465,bool),X7466,hAPP(fun(X7465,X7466),fun(fun(X7465,bool),X7466),big_co1399186613setsum(X7465,X7466),hAPP(X7466,fun(X7465,X7466),combk(X7466,X7465),zero_zero(X7466))),X7467) = zero_zero(X7466) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_979_setsum__0])])]) ).

fof(i_0_2504,plain,
    ! [X4465,X4466] : hBOOL(hAPP(fun(X4465,bool),bool,hAPP(fun(X4465,bool),fun(fun(X4465,bool),bool),ord_less_eq(fun(X4465,bool)),X4466),top_top(fun(X4465,bool)))),
    inference(variable_rename,[status(thm)],[fact_162_subset__UNIV]) ).

cnf(i_0_2505,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_1415]) ).

cnf(i_0_2506,plain,
    ( 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))) = top_top(fun(X1,bool))
    | ti(X1,esk130_3(X2,X1,X3)) != hAPP(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1390]) ).

fof(i_0_2507,plain,
    ! [X5204,X5205] :
      ( ( X5204 = zero_zero(nat)
        | X5204 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X5205 = hAPP(nat,nat,suc,zero_zero(nat))
        | X5204 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X5204 = zero_zero(nat)
        | X5205 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X5205 = hAPP(nat,nat,suc,zero_zero(nat))
        | X5205 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X5204 != hAPP(nat,nat,suc,zero_zero(nat))
        | X5205 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) = hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X5204 != zero_zero(nat)
        | X5205 != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5204),X5205) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_411_add__is__1])])]) ).

fof(i_0_2508,plain,
    ! [X5206,X5207] :
      ( ( X5206 = zero_zero(nat)
        | X5206 = 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),X5206),X5207) )
      & ( X5207 = hAPP(nat,nat,suc,zero_zero(nat))
        | X5206 = 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),X5206),X5207) )
      & ( X5206 = zero_zero(nat)
        | X5207 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5206),X5207) )
      & ( X5207 = hAPP(nat,nat,suc,zero_zero(nat))
        | X5207 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5206),X5207) )
      & ( X5206 != hAPP(nat,nat,suc,zero_zero(nat))
        | X5207 != zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5206),X5207) )
      & ( X5206 != zero_zero(nat)
        | X5207 != 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),X5206),X5207) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_412_one__is__add])])]) ).

fof(i_0_2509,plain,
    ! [X4687,X4688] : hBOOL(hAPP(fun(X4687,bool),bool,hAPP(fun(X4687,bool),fun(fun(X4687,bool),bool),ord_less_eq(fun(X4687,bool)),X4688),X4688)),
    inference(variable_rename,[status(thm)],[fact_213_subset__refl]) ).

cnf(i_0_2510,hypothesis,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),f) = f,
    inference(split_conjunct,[status(thm)],[tsy_v_F_res]) ).

cnf(i_0_2511,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omktop_res]) ).

cnf(i_0_2512,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_Omkbot_res]) ).

cnf(i_0_2513,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_1394]) ).

fof(i_0_2514,plain,
    ! [X4368,X4369] : hBOOL(hAPP(fun(X4368,bool),bool,hAPP(fun(X4368,X4368),fun(fun(X4368,bool),bool),inj_on(X4368,X4368),combi(X4368)),X4369)),
    inference(variable_rename,[status(thm)],[fact_142_inj__on__id2]) ).

fof(i_0_2515,plain,
    ! [X6360] : hBOOL(hAPP(fun(X6360,bool),bool,hAPP(X6360,fun(fun(X6360,bool),bool),member(X6360),esk148_1(X6360)),top_top(fun(X6360,bool)))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_714_UNIV__witness])]) ).

fof(i_0_2516,plain,
    ! [X4009,X4010] : hBOOL(hAPP(fun(X4009,bool),bool,hAPP(X4009,fun(fun(X4009,bool),bool),member(X4009),X4010),top_top(fun(X4009,bool)))),
    inference(variable_rename,[status(thm)],[fact_27_iso__tuple__UNIV__I]) ).

fof(i_0_2517,plain,
    ! [X4007,X4008] : hBOOL(hAPP(fun(X4007,bool),bool,hAPP(X4007,fun(fun(X4007,bool),bool),member(X4007),X4008),top_top(fun(X4007,bool)))),
    inference(variable_rename,[status(thm)],[fact_26_UNIV__I]) ).

cnf(i_0_2518,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_1416]) ).

fof(i_0_2519,plain,
    ! [X5192] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X5192)),
    inference(variable_rename,[status(thm)],[fact_407_inj__Suc]) ).

cnf(i_0_2520,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_1389]) ).

fof(i_0_2521,plain,
    ! [X5698] :
      ( ~ ring_1(X5698)
      | hBOOL(hAPP(fun(X5698,bool),bool,hAPP(X5698,fun(fun(X5698,bool),bool),member(X5698),zero_zero(X5698)),ring_1_Ints(X5698))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_535_Ints__0])]) ).

fof(i_0_2522,plain,
    ! [X5702] :
      ( ~ ring_1(X5702)
      | hBOOL(hAPP(fun(X5702,bool),bool,hAPP(X5702,fun(fun(X5702,bool),bool),member(X5702),one_one(X5702)),ring_1_Ints(X5702))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_537_Ints__1])]) ).

fof(i_0_2523,plain,
    ! [X6143,X6144] :
      ( ( X6143 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6143),X6144) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X6144 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6143),X6144) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X6143 != hAPP(nat,nat,suc,zero_zero(nat))
        | X6144 != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6143),X6144) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_659_mult__eq__1__iff])])]) ).

fof(i_0_2524,plain,
    ! [X4923] :
      ( ( ~ hBOOL(hAPP(fun(option(X4923),bool),bool,finite_finite_1(option(X4923)),top_top(fun(option(X4923),bool))))
        | hBOOL(hAPP(fun(X4923,bool),bool,finite_finite_1(X4923),top_top(fun(X4923,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X4923,bool),bool,finite_finite_1(X4923),top_top(fun(X4923,bool))))
        | hBOOL(hAPP(fun(option(X4923),bool),bool,finite_finite_1(option(X4923)),top_top(fun(option(X4923),bool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_294_finite__option__UNIV])]) ).

cnf(i_0_2525,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ti(X1,X3) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1417]) ).

cnf(i_0_2526,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ti(X1,X3) = zero_zero(X1)
    | ~ no_zero_divisors(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1418]) ).

cnf(i_0_2527,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ti(X1,X3) = zero_zero(X1)
    | ~ no_zero_divisors(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1419]) ).

cnf(i_0_2528,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_1420]) ).

cnf(i_0_2529,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_1421]) ).

cnf(i_0_2530,plain,
    ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),comp(X1,X2,X3)) = comp(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_1422]) ).

cnf(i_0_2531,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_1423]) ).

fof(i_0_2532,plain,
    ! [X5084] :
      ( ~ linordered_semidom(X5084)
      | hBOOL(hAPP(X5084,bool,hAPP(X5084,fun(X5084,bool),ord_less_eq(X5084),zero_zero(X5084)),one_one(X5084))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_352_zero__le__one])]) ).

fof(i_0_2533,plain,
    ! [X5086] :
      ( ~ linordered_semidom(X5086)
      | hBOOL(hAPP(X5086,bool,hAPP(X5086,fun(X5086,bool),ord_less(X5086),zero_zero(X5086)),one_one(X5086))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_354_zero__less__one])]) ).

cnf(i_0_2534,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
    | ti(X1,X2) != top_top(X1)
    | ti(X1,X3) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1424]) ).

cnf(i_0_2535,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_1425]) ).

cnf(i_0_2536,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_1426]) ).

cnf(i_0_2537,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1427]) ).

fof(i_0_2538,plain,
    ! [X6880,X6881,X6882] :
      ( ~ lattice(X6880)
      | hAPP(X6880,X6880,hAPP(X6880,fun(X6880,X6880),semilattice_sup_sup(X6880),X6881),X6882) = hAPP(X6880,X6880,hAPP(X6880,fun(X6880,X6880),semilattice_sup_sup(X6880),X6882),X6881) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_825_inf__sup__aci_I5_J])])]) ).

fof(i_0_2539,plain,
    ! [X6883,X6884,X6885] :
      ( ~ semilattice_sup(X6883)
      | hAPP(X6883,X6883,hAPP(X6883,fun(X6883,X6883),semilattice_sup_sup(X6883),X6884),X6885) = hAPP(X6883,X6883,hAPP(X6883,fun(X6883,X6883),semilattice_sup_sup(X6883),X6885),X6884) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_826_sup__commute])])]) ).

fof(i_0_2540,plain,
    ! [X6877,X6878,X6879] :
      ( ~ semilattice_sup(X6877)
      | hAPP(X6877,X6877,hAPP(X6877,fun(X6877,X6877),semilattice_sup_sup(X6877),X6878),X6879) = hAPP(X6877,X6877,hAPP(X6877,fun(X6877,X6877),semilattice_sup_sup(X6877),X6879),X6878) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_824_sup_Ocommute])])]) ).

fof(i_0_2541,plain,
    ! [X7337,X7338,X7339] :
      ( ~ lattice(X7337)
      | hAPP(X7337,X7337,hAPP(X7337,fun(X7337,X7337),semilattice_inf_inf(X7337),X7338),X7339) = hAPP(X7337,X7337,hAPP(X7337,fun(X7337,X7337),semilattice_inf_inf(X7337),X7339),X7338) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_948_inf__sup__aci_I1_J])])]) ).

fof(i_0_2542,plain,
    ! [X7340,X7341,X7342] :
      ( ~ semilattice_inf(X7340)
      | hAPP(X7340,X7340,hAPP(X7340,fun(X7340,X7340),semilattice_inf_inf(X7340),X7341),X7342) = hAPP(X7340,X7340,hAPP(X7340,fun(X7340,X7340),semilattice_inf_inf(X7340),X7342),X7341) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_949_inf_Ocommute])])]) ).

fof(i_0_2543,plain,
    ! [X7334,X7335,X7336] :
      ( ~ semilattice_inf(X7334)
      | hAPP(X7334,X7334,hAPP(X7334,fun(X7334,X7334),semilattice_inf_inf(X7334),X7335),X7336) = hAPP(X7334,X7334,hAPP(X7334,fun(X7334,X7334),semilattice_inf_inf(X7334),X7336),X7335) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_947_inf__commute])])]) ).

fof(i_0_2544,plain,
    ! [X5903,X5904,X5905] :
      ( ~ comm_semiring_1(X5903)
      | hAPP(X5903,X5903,hAPP(X5903,fun(X5903,X5903),times_times(X5903),X5904),X5905) = hAPP(X5903,X5903,hAPP(X5903,fun(X5903,X5903),times_times(X5903),X5905),X5904) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).

fof(i_0_2545,plain,
    ! [X5289,X5290,X5291] :
      ( ~ comm_semiring_1(X5289)
      | hAPP(X5289,X5289,hAPP(X5289,fun(X5289,X5289),plus_plus(X5289),X5290),X5291) = hAPP(X5289,X5289,hAPP(X5289,fun(X5289,X5289),plus_plus(X5289),X5291),X5290) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).

fof(i_0_2546,plain,
    ! [X4323,X4324] :
      ( ~ top(X4323)
      | hBOOL(hAPP(X4323,bool,hAPP(X4323,fun(X4323,bool),ord_less_eq(X4323),X4324),top_top(X4323))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_top__greatest])])]) ).

fof(i_0_2547,plain,
    ! [X4995,X4996] : hAPP(fun(X4995,bool),fun(sum_sum(X4996,X4995),bool),hAPP(fun(X4996,bool),fun(fun(X4995,bool),fun(sum_sum(X4996,X4995),bool)),sum_Plus(X4996,X4995),top_top(fun(X4996,bool))),top_top(fun(X4995,bool))) = top_top(fun(sum_sum(X4996,X4995),bool)),
    inference(variable_rename,[status(thm)],[fact_313_UNIV__Plus__UNIV]) ).

fof(i_0_2548,plain,
    ! [X4239,X4240,X4241] :
      ( ~ preorder(X4239)
      | X4240 != X4241
      | hBOOL(hAPP(X4239,bool,hAPP(X4239,fun(X4239,bool),ord_less_eq(X4239),X4240),X4241)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_107_order__eq__refl])])]) ).

fof(i_0_2549,plain,
    ! [X4187,X4188] :
      ( ~ preorder(X4187)
      | hBOOL(hAPP(X4187,bool,hAPP(X4187,fun(X4187,bool),ord_less_eq(X4187),X4188),X4188)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_order__refl])])]) ).

cnf(i_0_2550,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),restrict(X1,X2)) = restrict(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1428]) ).

fof(i_0_2551,plain,
    ! [X5040] :
      ( X5040 = zero_zero(nat)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_333_gr0I])]) ).

fof(i_0_2552,plain,
    ! [X5048] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X5048)),
    inference(variable_rename,[status(thm)],[fact_339_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_2553,plain,
    ! [X5020] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X5020)),
    inference(variable_rename,[status(thm)],[fact_320_le0]) ).

fof(i_0_2554,plain,
    ! [X7494,X7495,X7496,X7497] :
      ( ~ comm_monoid_add(X7495)
      | hBOOL(hAPP(fun(X7494,bool),bool,finite_finite_1(X7494),X7497))
      | hAPP(fun(X7494,bool),X7495,hAPP(fun(X7494,X7495),fun(fun(X7494,bool),X7495),big_co1399186613setsum(X7494,X7495),X7496),X7497) = zero_zero(X7495) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1429])])]) ).

fof(i_0_2555,plain,
    ! [X7490,X7491,X7492,X7493] :
      ( ~ comm_monoid_add(X7491)
      | hBOOL(hAPP(fun(X7490,bool),bool,finite_finite_1(X7490),X7493))
      | hAPP(fun(X7490,bool),X7491,hAPP(fun(X7490,X7491),fun(fun(X7490,bool),X7491),big_co1399186613setsum(X7490,X7491),X7492),X7493) = zero_zero(X7491) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1430])])]) ).

cnf(i_0_2556,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_1431]) ).

cnf(i_0_2557,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),top_top(fun(X1,bool))) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_1432]) ).

fof(i_0_2558,plain,
    ! [X4722,X4723] :
      ( X4722 != X4723
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4722),X4723)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_229_eq__imp__le])]) ).

fof(i_0_2559,plain,
    ! [X4719] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4719),X4719)),
    inference(variable_rename,[status(thm)],[fact_227_le__refl]) ).

fof(i_0_2560,plain,
    ! [X6296,X6297] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6296),X6297) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6297),X6296),
    inference(variable_rename,[status(thm)],[fact_702_nat__mult__commute]) ).

fof(i_0_2561,plain,
    ! [X4705,X4706] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4705),X4706) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4706),X4705),
    inference(variable_rename,[status(thm)],[fact_222_nat__add__commute]) ).

fof(i_0_2562,plain,
    ! [X7618,X7619] :
      ( ~ hBOOL(X7619)
      | ~ hBOOL(X7618)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X7619),X7618)) ),
    inference(variable_rename,[status(thm)],[i_0_1433]) ).

fof(i_0_2563,plain,
    ! [X7624,X7625] :
      ( ~ hBOOL(X7625)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X7625),X7624)) ),
    inference(variable_rename,[status(thm)],[i_0_1434]) ).

fof(i_0_2564,plain,
    ! [X7626,X7627] :
      ( ~ hBOOL(X7627)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X7626),X7627)) ),
    inference(variable_rename,[status(thm)],[i_0_1435]) ).

cnf(i_0_2565,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_1436]) ).

cnf(i_0_2566,plain,
    ( ti(X1,X2) = top_top(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1424]) ).

cnf(i_0_2567,plain,
    ( ti(X1,X2) = top_top(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1424]) ).

cnf(i_0_2568,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_1437]) ).

cnf(i_0_2569,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_1438]) ).

cnf(i_0_2570,plain,
    ti(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OProf_res]) ).

cnf(i_0_2571,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_1439]) ).

cnf(i_0_2572,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_1440]) ).

cnf(i_0_2573,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_1441]) ).

cnf(i_0_2574,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_1416]) ).

cnf(i_0_2575,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1442]) ).

cnf(i_0_2576,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1443]) ).

cnf(i_0_2577,plain,
    ( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1442]) ).

cnf(i_0_2578,plain,
    ( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1443]) ).

cnf(i_0_2579,plain,
    ti(fun(X1,fun(fun(nat,X1),fun(nat,X1))),nat_case(X1)) = nat_case(X1),
    inference(split_conjunct,[status(thm)],[i_0_1444]) ).

fof(i_0_2580,plain,
    ! [X6810,X6811] : hAPP(fun(X6810,bool),fun(X6810,bool),hAPP(fun(X6810,bool),fun(fun(X6810,bool),fun(X6810,bool)),semilattice_sup_sup(fun(X6810,bool)),top_top(fun(X6810,bool))),X6811) = top_top(fun(X6810,bool)),
    inference(variable_rename,[status(thm)],[fact_806_Un__UNIV__left]) ).

cnf(i_0_2581,plain,
    ti(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),finite_psubset(X1)) = finite_psubset(X1),
    inference(split_conjunct,[status(thm)],[i_0_1445]) ).

fof(i_0_2582,plain,
    ! [X6812,X6813] : hAPP(fun(X6812,bool),fun(X6812,bool),hAPP(fun(X6812,bool),fun(fun(X6812,bool),fun(X6812,bool)),semilattice_sup_sup(fun(X6812,bool)),X6813),top_top(fun(X6812,bool))) = top_top(fun(X6812,bool)),
    inference(variable_rename,[status(thm)],[fact_807_Un__UNIV__right]) ).

fof(i_0_2583,plain,
    ! [X5979,X5980] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5979),X5980) != zero_zero(nat)
        | X5979 = zero_zero(nat)
        | X5980 = zero_zero(nat) )
      & ( X5979 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5979),X5980) = zero_zero(nat) )
      & ( X5980 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5979),X5980) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_609_mult__is__0])])]) ).

fof(i_0_2584,plain,
    ! [X6169,X6170] :
      ( X6169 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X6169),X6170)
      | X6170 = one_one(nat)
      | X6169 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_669_mult__eq__self__implies__10])]) ).

fof(i_0_2585,plain,
    ! [X5043,X5044] :
      ( ( X5043 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5043),X5044) != zero_zero(nat) )
      & ( X5044 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5043),X5044) != zero_zero(nat) )
      & ( X5043 != zero_zero(nat)
        | X5044 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5043),X5044) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_336_add__is__0])])]) ).

fof(i_0_2586,plain,
    ! [X5958,X5959] :
      ( ( X5958 = one_one(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5958),X5959) != one_one(nat) )
      & ( X5959 = one_one(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5958),X5959) != one_one(nat) )
      & ( X5958 != one_one(nat)
        | X5959 != one_one(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5958),X5959) = one_one(nat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_600_nat__mult__eq__1__iff])])]) ).

fof(i_0_2587,plain,
    ! [X5961,X5962] :
      ( ( X5961 = one_one(nat)
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5961),X5962) )
      & ( X5962 = one_one(nat)
        | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5961),X5962) )
      & ( X5961 != one_one(nat)
        | X5962 != one_one(nat)
        | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5961),X5962) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_602_nat__1__eq__mult__iff])])]) ).

fof(i_0_2588,plain,
    ! [X5045,X5046] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5045),X5046) != X5045
      | X5046 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_337_add__eq__self__zero])]) ).

cnf(i_0_2589,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1417]) ).

cnf(i_0_2590,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1417]) ).

cnf(i_0_2591,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_1437]) ).

cnf(i_0_2592,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_1438]) ).

cnf(i_0_2593,plain,
    hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_1446]) ).

cnf(i_0_2594,plain,
    ( ti(fun(fun(X2,X1),fun(fun(X2,bool),X1)),big_co1399186613setsum(X2,X1)) = big_co1399186613setsum(X2,X1)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1447]) ).

cnf(i_0_2595,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),bool)),extensional(X1,X2)) = extensional(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1448]) ).

cnf(i_0_2596,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_1449]) ).

cnf(i_0_2597,plain,
    ti(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),measure(X1)) = measure(X1),
    inference(split_conjunct,[status(thm)],[i_0_1450]) ).

cnf(i_0_2598,plain,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_1451]) ).

cnf(i_0_2599,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = ti(X1,X2)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1452]) ).

cnf(i_0_2600,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
    | ~ comm_monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1453]) ).

cnf(i_0_2601,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1454]) ).

cnf(i_0_2602,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = ti(X1,X2)
    | ~ monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1455]) ).

cnf(i_0_2603,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_1456]) ).

cnf(i_0_2604,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_1457]) ).

cnf(i_0_2605,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_1458]) ).

cnf(i_0_2606,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = ti(X1,X2)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1459]) ).

cnf(i_0_2607,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
    | ~ comm_monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1460]) ).

cnf(i_0_2608,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1461]) ).

cnf(i_0_2609,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = ti(X1,X2)
    | ~ monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1462]) ).

cnf(i_0_2610,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_1463]) ).

cnf(i_0_2611,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_1464]) ).

cnf(i_0_2612,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_1465]) ).

cnf(i_0_2613,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1466]) ).

cnf(i_0_2614,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1467]) ).

cnf(i_0_2615,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = ti(X1,X2)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1468]) ).

cnf(i_0_2616,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1469]) ).

cnf(i_0_2617,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1470]) ).

cnf(i_0_2618,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = ti(X1,X2)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1471]) ).

cnf(i_0_2619,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
    | ~ ab_sem1668676832m_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1472]) ).

cnf(i_0_2620,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = ti(X1,X2)
    | ~ ab_sem1668676832m_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1473]) ).

fof(i_0_2621,plain,
    ! [X5267] : hAPP(nat,nat,suc,X5267) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X5267),
    inference(variable_rename,[status(thm)],[fact_437_Suc__eq__plus1__left]) ).

fof(i_0_2622,plain,
    ! [X5266] : hAPP(nat,nat,suc,X5266) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5266),one_one(nat)),
    inference(variable_rename,[status(thm)],[fact_436_Suc__eq__plus1]) ).

fof(i_0_2623,plain,
    ! [X7020] : hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X7020)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X7020),
    inference(variable_rename,[status(thm)],[fact_864_atLeast__Suc__greaterThan]) ).

fof(i_0_2624,plain,
    ! [X5232] : hAPP(nat,fun(nat,bool),ord_less(nat),X5232) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X5232)),
    inference(variable_rename,[status(thm)],[fact_424_less__eq__Suc__le__raw]) ).

cnf(i_0_2625,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_1474]) ).

cnf(i_0_2626,plain,
    ti(X1,ti(X1,X2)) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1475]) ).

cnf(i_0_2627,plain,
    hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_1476]) ).

cnf(i_0_2628,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_1477]) ).

fof(i_0_2629,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(fof_simplification,[status(thm)],[fact_286_infinite__UNIV__nat]) ).

cnf(i_0_2630,plain,
    ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    inference(split_conjunct,[status(thm)],[i_0_1478]) ).

cnf(i_0_2631,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1479]) ).

cnf(i_0_2632,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1480]) ).

cnf(i_0_2633,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1481]) ).

cnf(i_0_2634,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastAtMost(X1)) = ord_atLeastAtMost(X1)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1482]) ).

cnf(i_0_2635,plain,
    ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    inference(split_conjunct,[status(thm)],[i_0_1483]) ).

fof(i_0_2636,plain,
    ! [X4131] : top_top(fun(X4131,bool)) = hAPP(fun(X4131,bool),fun(X4131,bool),collect(X4131),hAPP(bool,fun(X4131,bool),combk(bool,X4131),fTrue)),
    inference(variable_rename,[status(thm)],[fact_78_UNIV__def]) ).

cnf(i_0_2637,plain,
    ti(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    inference(split_conjunct,[status(thm)],[tsy_c_Arrow__Order__Mirabelle__atbwwtcaxb_OLin_res]) ).

cnf(i_0_2638,hypothesis,
    ti(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),p) = p,
    inference(split_conjunct,[status(thm)],[tsy_v_P_____res]) ).

fof(i_0_2639,plain,
    ! [X5090,X5091] :
      ( hBOOL(hAPP(fun(X5090,bool),bool,finite_finite_1(X5090),X5091))
      | hAPP(fun(X5090,bool),nat,finite_card(X5090),X5091) = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1484])]) ).

fof(i_0_2640,plain,
    ! [X6977,X6978] :
      ( ~ bounded_lattice_top(X6977)
      | hAPP(X6977,X6977,hAPP(X6977,fun(X6977,X6977),semilattice_sup_sup(X6977),top_top(X6977)),X6978) = top_top(X6977) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_852_sup__top__left])])]) ).

fof(i_0_2641,plain,
    ! [X5937,X5938] :
      ( ~ comm_semiring_1(X5937)
      | hAPP(X5937,X5937,hAPP(X5937,fun(X5937,X5937),times_times(X5937),zero_zero(X5937)),X5938) = zero_zero(X5937) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])]) ).

fof(i_0_2642,plain,
    ! [X5952,X5953] :
      ( ~ mult_zero(X5952)
      | hAPP(X5952,X5952,hAPP(X5952,fun(X5952,X5952),times_times(X5952),zero_zero(X5952)),X5953) = zero_zero(X5952) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_598_mult__zero__left])])]) ).

fof(i_0_2643,plain,
    ! [X6979,X6980] :
      ( ~ bounded_lattice_top(X6979)
      | hAPP(X6979,X6979,hAPP(X6979,fun(X6979,X6979),semilattice_sup_sup(X6979),X6980),top_top(X6979)) = top_top(X6979) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_853_sup__top__right])])]) ).

fof(i_0_2644,plain,
    ! [X5939,X5940] :
      ( ~ comm_semiring_1(X5939)
      | hAPP(X5939,X5939,hAPP(X5939,fun(X5939,X5939),times_times(X5939),X5940),zero_zero(X5939)) = zero_zero(X5939) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])]) ).

fof(i_0_2645,plain,
    ! [X5950,X5951] :
      ( ~ mult_zero(X5950)
      | hAPP(X5950,X5950,hAPP(X5950,fun(X5950,X5950),times_times(X5950),X5951),zero_zero(X5950)) = zero_zero(X5950) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_597_mult__zero__right])])]) ).

fof(i_0_2646,plain,
    ! [X5982] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X5982) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_611_mult__0]) ).

fof(i_0_2647,plain,
    ! [X5963] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X5963) = X5963,
    inference(variable_rename,[status(thm)],[fact_603_nat__mult__1]) ).

fof(i_0_2648,plain,
    ! [X5041] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X5041) = X5041,
    inference(variable_rename,[status(thm)],[fact_334_plus__nat_Oadd__0]) ).

cnf(i_0_2649,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(ti(bool,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1485]) ).

fof(i_0_2650,plain,
    ! [X5981] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5981),zero_zero(nat)) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_610_mult__0__right]) ).

fof(i_0_2651,plain,
    ! [X5960] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X5960),one_one(nat)) = X5960,
    inference(variable_rename,[status(thm)],[fact_601_nat__mult__1__right]) ).

fof(i_0_2652,plain,
    ! [X5042] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5042),zero_zero(nat)) = X5042,
    inference(variable_rename,[status(thm)],[fact_335_Nat_Oadd__0__right]) ).

fof(i_0_2653,plain,
    ! [X7591] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X7591))
      | ~ hBOOL(X7591) ),
    inference(variable_rename,[status(thm)],[i_0_1486]) ).

fof(i_0_2654,plain,
    ! [X5140,X5141] :
      ( ( hAPP(nat,nat,suc,X5140) != hAPP(nat,nat,suc,X5141)
        | X5140 = X5141 )
      & ( X5140 != X5141
        | hAPP(nat,nat,suc,X5140) = hAPP(nat,nat,suc,X5141) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_nat_Oinject])]) ).

fof(i_0_2655,plain,
    ! [X5138,X5139] :
      ( hAPP(nat,nat,suc,X5138) != hAPP(nat,nat,suc,X5139)
      | X5138 = X5139 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_376_Suc__inject])]) ).

cnf(i_0_2656,plain,
    ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    inference(split_conjunct,[status(thm)],[i_0_1487]) ).

fof(i_0_2657,plain,
    ! [X4928] :
      ( ~ finite_finite(X4928)
      | hBOOL(hAPP(fun(X4928,bool),bool,finite_finite_1(X4928),top_top(fun(X4928,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_297_finite__UNIV])]) ).

cnf(i_0_2658,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[i_0_1488]) ).

cnf(i_0_2659,plain,
    ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1489]) ).

fof(i_0_2660,plain,
    ! [X4005,X4006] : hBOOL(hAPP(X4005,bool,top_top(fun(X4005,bool)),X4006)),
    inference(variable_rename,[status(thm)],[fact_25_top1I]) ).

cnf(i_0_2661,plain,
    ( ti(fun(X1,fun(X1,X1)),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1490]) ).

cnf(i_0_2662,plain,
    ( ti(fun(X1,fun(X1,X1)),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1491]) ).

cnf(i_0_2663,plain,
    ( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
    | ~ no_zero_divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1492]) ).

cnf(i_0_2664,plain,
    ( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
    | ~ mult_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1493]) ).

cnf(i_0_2665,plain,
    ( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
    | ~ ab_semigroup_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1494]) ).

cnf(i_0_2666,plain,
    ( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
    | ~ monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1495]) ).

cnf(i_0_2667,plain,
    ( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
    | ~ semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1496]) ).

cnf(i_0_2668,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1497]) ).

cnf(i_0_2669,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1498]) ).

cnf(i_0_2670,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1499]) ).

fof(i_0_2671,plain,
    ! [X4911,X4912] :
      ( ~ finite_finite(X4911)
      | hBOOL(hAPP(fun(X4911,bool),bool,finite_finite_1(X4911),X4912)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_288_finite])])]) ).

fof(i_0_2672,plain,
    ! [X4909,X4910] :
      ( ~ finite_finite(X4909)
      | hBOOL(hAPP(fun(X4909,bool),bool,finite_finite_1(X4909),X4910)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_finite__code])])]) ).

cnf(i_0_2673,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_greaterThan(X1)) = ord_greaterThan(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1500]) ).

cnf(i_0_2674,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_atLeast(X1)) = ord_atLeast(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1501]) ).

cnf(i_0_2675,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1502]) ).

cnf(i_0_2676,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1503]) ).

cnf(i_0_2677,plain,
    ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    inference(split_conjunct,[status(thm)],[i_0_1504]) ).

cnf(i_0_2678,plain,
    ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    inference(split_conjunct,[status(thm)],[i_0_1505]) ).

cnf(i_0_2679,plain,
    ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    inference(split_conjunct,[status(thm)],[i_0_1506]) ).

cnf(i_0_2680,hypothesis,
    ( hBOOL(ti(bool,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1485]) ).

cnf(i_0_2681,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lba) = lba,
    inference(split_conjunct,[status(thm)],[tsy_v_Lba_____res]) ).

cnf(i_0_2682,plain,
    ti(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),lab) = lab,
    inference(split_conjunct,[status(thm)],[tsy_v_Lab_____res]) ).

cnf(i_0_2683,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(split_conjunct,[status(thm)],[tsy_c_fdisj_res]) ).

cnf(i_0_2684,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(split_conjunct,[status(thm)],[tsy_c_fconj_res]) ).

cnf(i_0_2685,plain,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(split_conjunct,[status(thm)],[i_0_1507]) ).

cnf(i_0_2686,plain,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(split_conjunct,[status(thm)],[i_0_1508]) ).

cnf(i_0_2687,plain,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(split_conjunct,[status(thm)],[i_0_1509]) ).

fof(i_0_2688,plain,
    ! [X7592] :
      ( hBOOL(X7592)
      | hBOOL(hAPP(bool,bool,fNot,X7592)) ),
    inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).

fof(i_0_2689,plain,
    ! [X5147] : hAPP(nat,nat,suc,X5147) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_383_Suc__not__Zero]) ).

fof(i_0_2690,plain,
    ! [X5146] : hAPP(nat,nat,suc,X5146) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_382_nat_Osimps_I3_J]) ).

fof(i_0_2691,plain,
    ! [X5144] : hAPP(nat,nat,suc,X5144) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[fact_380_Suc__neq__Zero]) ).

fof(i_0_2692,plain,
    ! [X5149] : zero_zero(nat) != hAPP(nat,nat,suc,X5149),
    inference(variable_rename,[status(thm)],[fact_385_Zero__not__Suc]) ).

fof(i_0_2693,plain,
    ! [X5148] : zero_zero(nat) != hAPP(nat,nat,suc,X5148),
    inference(variable_rename,[status(thm)],[fact_384_nat_Osimps_I2_J]) ).

fof(i_0_2694,plain,
    ! [X5145] : zero_zero(nat) != hAPP(nat,nat,suc,X5145),
    inference(variable_rename,[status(thm)],[fact_381_Zero__neq__Suc]) ).

fof(i_0_2695,plain,
    ! [X5142] : hAPP(nat,nat,suc,X5142) != X5142,
    inference(variable_rename,[status(thm)],[fact_378_Suc__n__not__n]) ).

fof(i_0_2696,plain,
    ! [X5143] : X5143 != hAPP(nat,nat,suc,X5143),
    inference(variable_rename,[status(thm)],[fact_379_n__not__Suc__n]) ).

cnf(i_0_2697,plain,
    ti(fun(X1,X1),combi(X1)) = combi(X1),
    inference(split_conjunct,[status(thm)],[i_0_1510]) ).

cnf(i_0_2698,plain,
    ( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1511]) ).

cnf(i_0_2699,plain,
    ti(fun(nat,nat),size_size(nat)) = size_size(nat),
    inference(split_conjunct,[status(thm)],[tsy_c_Nat_Osize__class_Osize_res]) ).

cnf(i_0_2700,plain,
    ti(fun(nat,nat),nat_size) = nat_size,
    inference(split_conjunct,[status(thm)],[tsy_c_Nat_Onat_Onat__size_res]) ).

cnf(i_0_2701,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(split_conjunct,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

cnf(i_0_2702,plain,
    ti(fun(bool,nat),bool_size) = bool_size,
    inference(split_conjunct,[status(thm)],[tsy_c_HOL_Obool_Obool__size_res]) ).

cnf(i_0_2703,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(split_conjunct,[status(thm)],[tsy_c_fNot_res]) ).

cnf(i_0_2704,plain,
    ti(fun(arrow_1998540521e_indi,nat),h) = h,
    inference(split_conjunct,[status(thm)],[tsy_v_h_____res]) ).

fof(i_0_2705,plain,
    ! [X4017,X4018,X4019] :
      ( ~ top(X4018)
      | hAPP(X4017,X4018,top_top(fun(X4017,X4018)),X4019) = top_top(X4018) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_top__apply])])]) ).

cnf(i_0_2706,plain,
    ( ti(X1,top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1512]) ).

cnf(i_0_2707,plain,
    ( ti(X1,zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1513]) ).

cnf(i_0_2708,plain,
    ( ti(X1,one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1514]) ).

cnf(i_0_2709,plain,
    ti(X1,undefined(X1)) = undefined(X1),
    inference(split_conjunct,[status(thm)],[i_0_1515]) ).

fof(i_0_2710,plain,
    ! [X5279] :
      ( X5279 = zero_zero(nat)
      | X5279 = hAPP(nat,nat,suc,esk97_1(X5279)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_nat_Oexhaust])])]) ).

fof(i_0_2711,plain,
    ! [X5277] :
      ( X5277 = zero_zero(nat)
      | X5277 = hAPP(nat,nat,suc,esk96_1(X5277)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_441_not0__implies__Suc])])]) ).

fof(i_0_2712,plain,
    ! [X6510] : hAPP(nat,nat,size_size(nat),X6510) = X6510,
    inference(variable_rename,[status(thm)],[fact_741_nat__size]) ).

cnf(i_0_2713,plain,
    ti(nat,n) = n,
    inference(split_conjunct,[status(thm)],[tsy_v_n_____res]) ).

cnf(i_0_2714,plain,
    ti(bool,fTrue) = fTrue,
    inference(split_conjunct,[status(thm)],[tsy_c_fTrue_res]) ).

cnf(i_0_2715,plain,
    ti(bool,fFalse) = fFalse,
    inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).

cnf(i_0_2716,plain,
    ti(arrow_2142409994le_alt,e) = e,
    inference(split_conjunct,[status(thm)],[tsy_v_e_____res]) ).

cnf(i_0_2717,hypothesis,
    ti(arrow_2142409994le_alt,d) = d,
    inference(split_conjunct,[status(thm)],[tsy_v_d_____res]) ).

cnf(i_0_2718,hypothesis,
    ti(arrow_2142409994le_alt,c) = c,
    inference(split_conjunct,[status(thm)],[tsy_v_c_____res]) ).

cnf(i_0_2719,plain,
    ti(arrow_2142409994le_alt,b) = b,
    inference(split_conjunct,[status(thm)],[tsy_v_b_____res]) ).

cnf(i_0_2720,plain,
    ti(arrow_2142409994le_alt,a) = a,
    inference(split_conjunct,[status(thm)],[tsy_v_a_____res]) ).

fof(i_0_2721,plain,
    ! [X7577,X7578] :
      ( ~ finite_finite(X7578)
      | ~ finite_finite(X7577)
      | finite_finite(sum_sum(X7577,X7578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite])]) ).

fof(i_0_2722,plain,
    ! [X7567,X7568] :
      ( ~ finite_finite(X7568)
      | ~ finite_finite(X7567)
      | finite_finite(fun(X7567,X7568)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite])]) ).

fof(i_0_2723,plain,
    ! [X7580,X7581] :
      ( ~ finite_finite(X7581)
      | ~ finite_finite(X7580)
      | finite_finite(product_prod(X7580,X7581)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod___Finite__Set_Ofinite])]) ).

fof(i_0_2724,plain,
    ! [X7555,X7556] :
      ( ~ bounded_lattice(X7556)
      | bounded_lattice(fun(X7555,X7556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Obounded__lattice])]) ).

fof(i_0_2725,plain,
    ! [X7563,X7564] :
      ( ~ distrib_lattice(X7564)
      | distrib_lattice(fun(X7563,X7564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Odistrib__lattice])]) ).

fof(i_0_2726,plain,
    ! [X7557,X7558] :
      ( ~ bounded_lattice(X7558)
      | bounded_lattice_top(fun(X7557,X7558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Obounded__lattice__top])]) ).

fof(i_0_2727,plain,
    ! [X7569,X7570] :
      ( ~ lattice(X7570)
      | lattice(fun(X7569,X7570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Olattice])]) ).

fof(i_0_2728,plain,
    ! [X7565,X7566] :
      ( ~ preorder(X7566)
      | preorder(fun(X7565,X7566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder])]) ).

fof(i_0_2729,plain,
    ! [X7571,X7572] :
      ( ~ order(X7572)
      | order(fun(X7571,X7572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder])]) ).

fof(i_0_2730,plain,
    ! [X7573,X7574] :
      ( ~ top(X7574)
      | top(fun(X7573,X7574)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Otop])]) ).

fof(i_0_2731,plain,
    ! [X7575,X7576] :
      ( ~ ord(X7576)
      | ord(fun(X7575,X7576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord])]) ).

fof(i_0_2732,plain,
    ! [X7559,X7560] :
      ( ~ lattice(X7560)
      | semilattice_sup(fun(X7559,X7560)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Osemilattice__sup])]) ).

fof(i_0_2733,plain,
    ! [X7561,X7562] :
      ( ~ lattice(X7562)
      | semilattice_inf(fun(X7561,X7562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun___Lattices_Osemilattice__inf])]) ).

fof(i_0_2734,plain,
    ! [X5034] :
      ( ~ zero_neq_one(X5034)
      | one_one(X5034) != zero_zero(X5034) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_one__neq__zero])]) ).

fof(i_0_2735,plain,
    ! [X5033] :
      ( ~ zero_neq_one(X5033)
      | zero_zero(X5033) != one_one(X5033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_327_zero__neq__one])]) ).

fof(i_0_2736,plain,
    ! [X7579] :
      ( ~ finite_finite(X7579)
      | finite_finite(option(X7579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option_Ooption___Finite__Set_Ofinite])]) ).

fof(i_0_2737,plain,
    ~ hBOOL(fFalse),
    inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).

cnf(i_0_2738,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X4),X7) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X5),X8)
    | hAPP(X1,X3,X4,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X3,X5,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | hAPP(X1,X1,X6,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X1,combi(X1),esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | hAPP(X1,X1,X2,hAPP(X1,X1,X6,esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X1,combi(X1),esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X6,esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X8))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X7))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool,hAPP(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool)),finite_folding_image(X3,X1),X9),X10),X11)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1516,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2739,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X4),X7) = hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),X11,X5),X8)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11)),X7))
    | hAPP(X1,X3,X4,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X3,X5,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | hAPP(X1,X1,X6,hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X1,combi(X1),esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X2,esk156_11(X1,X3,X4,X5,X2,X6,X7,X8,X9,X10,X11))),X7))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool,hAPP(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(fun(X1,X3),fun(fun(X1,bool),X3)),bool)),finite_folding_image(X3,X1),X9),X10),X11)) ),
    inference(rw,[status(thm)],[i_0_1518,c_0_1517]),
    [final] ).

cnf(i_0_2740,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X3),X7) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X4),X8)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)),X8))
    | hAPP(X1,X1,X5,hAPP(X1,X1,X6,esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))) != hAPP(X1,X1,combi(X1),esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,X6,esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11))),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X9),X10),X11)) ),
    inference(rw,[status(thm)],[i_0_1519,c_0_1517]),
    [final] ).

cnf(i_0_2741,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk156_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)),X8))
    | hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X4),X8) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X11,X3),X7)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk155_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)),X7))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X9),X10),X11)) ),
    inference(split_conjunct,[status(thm)],[i_0_1179]),
    [final] ).

cnf(i_0_2742,plain,
    ( hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9) = hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10)
    | hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | hAPP(X2,X1,X3,hAPP(X1,X2,X8,esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X1,X1,combi(X1),esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | ~ comm_monoid_mult(X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X10))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X8,esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X10))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1520,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2743,plain,
    ( hAPP(fun(X1,bool),X4,hAPP(X4,fun(fun(X1,bool),X4),hAPP(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X1,X4),fun(X4,fun(fun(X1,bool),X4))),finite_fold_image(X4,X1),times_times(X4)),X6),X5),X9) = hAPP(fun(X2,bool),X4,hAPP(X4,fun(fun(X2,bool),X4),hAPP(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4)),hAPP(fun(X4,fun(X4,X4)),fun(fun(X2,X4),fun(X4,fun(fun(X2,bool),X4))),finite_fold_image(X4,X2),times_times(X4)),X7),X5),X10)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk143_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10)),X9))
    | hAPP(X1,X4,X6,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X4,X7,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | hAPP(X1,X2,X8,hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))
    | ~ comm_monoid_mult(X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X10))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk144_10(X1,X2,X4,X5,X6,X7,X3,X8,X9,X10))),X9)) ),
    inference(rw,[status(thm)],[i_0_1521,c_0_1517]),
    [final] ).

cnf(i_0_2744,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk144_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
    | hAPP(X1,X2,X7,hAPP(X2,X1,X8,esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))) != hAPP(X2,X2,combi(X2),esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))
    | ~ comm_monoid_mult(X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X10))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X8,esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10))),X10)) ),
    inference(rw,[status(thm)],[i_0_1522,c_0_1517]),
    [final] ).

cnf(i_0_2745,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X4),X6)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X5),X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))),hAPP(X3,X1,X5,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),X7,esk157_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)),esk158_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),X7,esk159_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)),esk160_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool,hAPP(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool)),finite_folding_image(X1,X3),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2746,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),X7,esk157_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),esk158_9(X1,X2,X3,X4,X5,X6,X7,X8,X9))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),X7,esk159_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),esk160_9(X1,X2,X3,X4,X5,X6,X7,X8,X9))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2747,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk144_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X10))
    | hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),times_times(X3)),X6),X4),X10) = hAPP(fun(X2,bool),X3,hAPP(X3,fun(fun(X2,bool),X3),hAPP(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X2,X3),fun(X3,fun(fun(X2,bool),X3))),finite_fold_image(X3,X2),times_times(X3)),X5),X4),X9)
    | hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),esk143_10(X2,X1,X3,X4,X5,X6,X7,X8,X9,X10)),X9))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X10))
    | ~ comm_monoid_mult(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1181]),
    [final] ).

cnf(i_0_2748,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
    inference(split_conjunct,[status(thm)],[i_0_1524]),
    [final] ).

cnf(i_0_2749,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_2750,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_ind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),
    inference(split_conjunct,[status(thm)],[i_0_1526]),
    [final] ).

cnf(i_0_2751,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_1524]),
    [final] ).

cnf(i_0_2752,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_2753,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X4),X6)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X5),X6)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk158_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)),esk160_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))),hAPP(X3,X1,X5,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool,hAPP(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool)),finite_folding_image(X1,X3),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2754,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X4),X6)),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),X9,X5),X6)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk157_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)),esk159_9(X3,X1,X4,X5,X6,X2,X7,X8,X9)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))),hAPP(X3,X1,X5,esk161_9(X3,X1,X4,X5,X6,X2,X7,X8,X9))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool,hAPP(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X3,X1),fun(fun(X3,bool),X1)),bool)),finite_folding_image(X1,X3),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2755,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))) ),
    inference(split_conjunct,[status(thm)],[i_0_1526]),
    [final] ).

cnf(i_0_2756,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_2757,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_2758,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_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_2759,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1770777252_mktop),p)),e))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combs(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),fequal(nat)),h)),n))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),arrow_357225482_above),p)),c)),e))),hAPP(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(arrow_2142409994le_alt,fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combb(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1998540521e_indi),arrow_1622070166_mkbot),p)),e)))),arrow_301600364e_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_2760,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X4),X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk158_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),esk160_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2761,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk161_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X3),X5)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X9,X4),X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk157_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)),esk159_9(X1,X2,X3,X4,X5,X6,X7,X8,X9)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X8),X8))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X7),X8),X9)) ),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2762,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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_sup_sup(fun(product_prod(X2,X1),bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1527]),
    [final] ).

cnf(i_0_2763,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),X5),X6)),hAPP(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool),hAPP(fun(product_prod(X2,X1),bool),fun(fun(product_prod(X2,X1),bool),fun(product_prod(X2,X1),bool)),semilattice_inf_inf(fun(product_prod(X2,X1),bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X3)),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool))),combc(X2,fun(product_prod(X2,X1),bool),fun(X1,bool)),hAPP(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool))),fun(fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(X2,fun(fun(product_prod(X2,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(product_prod(X2,X1),bool),fun(X1,bool)),X2),combc(X1,fun(product_prod(X2,X1),bool),bool)),hAPP(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),fun(fun(X2,fun(X1,product_prod(X2,X1))),fun(X2,fun(X1,fun(fun(product_prod(X2,X1),bool),bool)))),combb(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool)),X2),hAPP(fun(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool)),fun(fun(X1,product_prod(X2,X1)),fun(X1,fun(fun(product_prod(X2,X1),bool),bool))),combb(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),X1),member(product_prod(X2,X1)))),product_Pair(X2,X1)))),X4)),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1528]),
    [final] ).

cnf(i_0_2764,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_sup_sup(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)))),X5)),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)))),X6)),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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_sup_sup(fun(product_prod(X1,X2),bool)),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_1527]),
    [final] ).

cnf(i_0_2765,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),fun(X1,fun(X2,bool))),semilattice_inf_inf(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)))),X5)),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)))),X6)),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)),hAPP(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool),hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),fun(product_prod(X1,X2),bool)),semilattice_inf_inf(fun(product_prod(X1,X2),bool)),X5),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_1528]),
    [final] ).

cnf(i_0_2766,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk142_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk142_7(X3,X1,X4,X5,X6,X2,X7))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk138_7(X3,X1,X4,X5,X6,X2,X7)),esk139_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk140_7(X3,X1,X4,X5,X6,X2,X7)),esk141_7(X3,X1,X4,X5,X6,X2,X7))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
    | ~ comm_monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2767,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk29_0),one_one(nat))))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_2768,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_1531]),
    [final] ).

cnf(i_0_2769,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_82_n_I3_J]),
    [final] ).

cnf(i_0_2770,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk29_0)) ),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_2771,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_1531]),
    [final] ).

cnf(i_0_2772,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_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_1532]),
    [final] ).

cnf(i_0_2773,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combc(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(arrow_1998540521e_indi,bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1998540521e_indi),if(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(nat,fun(arrow_1998540521e_indi,bool),hAPP(fun(arrow_1998540521e_indi,fun(nat,bool)),fun(nat,fun(arrow_1998540521e_indi,bool)),combc(arrow_1998540521e_indi,nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1998540521e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_301600364e_Prof)),
    inference(split_conjunct,[status(thm)],[i_0_1533]),
    [final] ).

cnf(i_0_2774,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_7(X1,X2,X3,X4,X5,X6,X7)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),esk138_7(X1,X2,X3,X4,X5,X6,X7)),esk139_7(X1,X2,X3,X4,X5,X6,X7))),hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),esk140_7(X1,X2,X3,X4,X5,X6,X7)),esk141_7(X1,X2,X3,X4,X5,X6,X7))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2775,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_1534]),
    [final] ).

cnf(i_0_2776,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_1534]),
    [final] ).

cnf(i_0_2777,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk139_7(X3,X1,X4,X5,X6,X2,X7)),esk141_7(X3,X1,X4,X5,X6,X2,X7)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk142_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk142_7(X3,X1,X4,X5,X6,X2,X7))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
    | ~ comm_monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2778,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X4),X7),X6)),hAPP(fun(X3,bool),X1,hAPP(X1,fun(fun(X3,bool),X1),hAPP(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X3,X1),fun(X1,fun(fun(X3,bool),X1))),finite_fold_image(X1,X3),times_times(X1)),X5),X7),X6)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,esk138_7(X3,X1,X4,X5,X6,X2,X7)),esk140_7(X3,X1,X4,X5,X6,X2,X7)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,hAPP(X3,X1,X4,esk142_7(X3,X1,X4,X5,X6,X2,X7))),hAPP(X3,X1,X5,esk142_7(X3,X1,X4,X5,X6,X2,X7))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),X2,X7),X7))
    | ~ comm_monoid_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2779,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,fun(X4,bool)),fun(X2,X1),hAPP(fun(X2,fun(fun(X4,bool),X1)),fun(fun(X2,fun(X4,bool)),fun(X2,X1)),combs(X2,fun(X4,bool),X1),hAPP(fun(X2,fun(X4,X1)),fun(X2,fun(fun(X4,bool),X1)),hAPP(fun(fun(X4,X1),fun(fun(X4,bool),X1)),fun(fun(X2,fun(X4,X1)),fun(X2,fun(fun(X4,bool),X1))),combb(fun(X4,X1),fun(fun(X4,bool),X1),X2),big_co1399186613setsum(X4,X1)),X6)),hAPP(fun(X2,fun(X4,bool)),fun(X2,fun(X4,bool)),hAPP(fun(fun(X4,bool),fun(X4,bool)),fun(fun(X2,fun(X4,bool)),fun(X2,fun(X4,bool))),combb(fun(X4,bool),fun(X4,bool),X2),collect(X4)),hAPP(fun(X2,fun(X4,bool)),fun(X2,fun(X4,bool)),hAPP(fun(fun(X4,bool),fun(X4,bool)),fun(fun(X2,fun(X4,bool)),fun(X2,fun(X4,bool))),combb(fun(X4,bool),fun(X4,bool),X2),hAPP(fun(X4,fun(bool,bool)),fun(fun(X4,bool),fun(X4,bool)),combs(X4,bool,bool),hAPP(fun(X4,bool),fun(X4,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X4,bool),fun(X4,fun(bool,bool))),combb(bool,fun(bool,bool),X4),fconj),hAPP(fun(X4,bool),fun(X4,bool),hAPP(fun(X4,fun(fun(X4,bool),bool)),fun(fun(X4,bool),fun(X4,bool)),combc(X4,fun(X4,bool),bool),member(X4)),X5)))),X7)))),X3) = hAPP(fun(X4,bool),X1,hAPP(fun(X4,X1),fun(fun(X4,bool),X1),big_co1399186613setsum(X4,X1),hAPP(fun(X4,fun(X2,bool)),fun(X4,X1),hAPP(fun(X4,fun(fun(X2,bool),X1)),fun(fun(X4,fun(X2,bool)),fun(X4,X1)),combs(X4,fun(X2,bool),X1),hAPP(fun(X4,fun(X2,X1)),fun(X4,fun(fun(X2,bool),X1)),hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X4,fun(X2,X1)),fun(X4,fun(fun(X2,bool),X1))),combb(fun(X2,X1),fun(fun(X2,bool),X1),X4),big_co1399186613setsum(X2,X1)),hAPP(fun(X2,fun(X4,X1)),fun(X4,fun(X2,X1)),combc(X2,X4,X1),X6))),hAPP(fun(X4,fun(X2,bool)),fun(X4,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X4,fun(X2,bool)),fun(X4,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X4),collect(X2)),hAPP(fun(X4,fun(X2,bool)),fun(X4,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X4,fun(X2,bool)),fun(X4,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X4),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X3)))),hAPP(fun(X2,fun(X4,bool)),fun(X4,fun(X2,bool)),combc(X2,X4,bool),X7))))),X5)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1535]),
    [final] ).

cnf(i_0_2780,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk152_8(X1,X2,X3,X4,X5,X6,X7,X8)),X5))
    | hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X8,X3),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X8,X4),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_2781,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),X6),X7)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X5,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X5,bool),X1)),fun(fun(X5,bool),fun(X2,X1)),combc(X2,fun(X5,bool),X1),hAPP(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1)),hAPP(fun(fun(X5,X1),fun(fun(X5,bool),X1)),fun(fun(X2,fun(X5,X1)),fun(X2,fun(fun(X5,bool),X1))),combb(fun(X5,X1),fun(fun(X5,bool),X1),X2),big_co1399186613setsum(X5,X1)),hAPP(fun(X5,X1),fun(X2,fun(X5,X1)),hAPP(fun(X2,fun(fun(X5,X1),fun(X5,X1))),fun(fun(X5,X1),fun(X2,fun(X5,X1))),combc(X2,fun(X5,X1),fun(X5,X1)),hAPP(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1))),hAPP(fun(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1))),fun(fun(X2,fun(X1,X1)),fun(X2,fun(fun(X5,X1),fun(X5,X1)))),combb(fun(X1,X1),fun(fun(X5,X1),fun(X5,X1)),X2),combb(X1,X1,X5)),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3))),X6))),X7)),X4)
    | ~ semiring_0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1537]),
    [final] ).

cnf(i_0_2782,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X8,X3),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X8,X4),X5)
    | hAPP(X1,X2,X3,esk152_8(X1,X2,X3,X4,X5,X6,X7,X8)) != hAPP(X1,X2,X4,esk152_8(X1,X2,X3,X4,X5,X6,X7,X8))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_1536]),
    [final] ).

cnf(i_0_2783,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_1538]),
    [final] ).

cnf(i_0_2784,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X3) = hAPP(fun(X5,bool),X1,hAPP(fun(X5,X1),fun(fun(X5,bool),X1),big_co1399186613setsum(X5,X1),hAPP(fun(X5,fun(X2,bool)),fun(X5,X1),hAPP(fun(fun(X2,bool),X1),fun(fun(X5,fun(X2,bool)),fun(X5,X1)),combb(fun(X2,bool),X1,X5),hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4)),hAPP(fun(X5,fun(X2,bool)),fun(X5,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X5,fun(X2,bool)),fun(X5,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X5),collect(X2)),hAPP(fun(X5,fun(X2,bool)),fun(X5,fun(X2,bool)),hAPP(fun(fun(X2,bool),fun(X2,bool)),fun(fun(X5,fun(X2,bool)),fun(X5,fun(X2,bool))),combb(fun(X2,bool),fun(X2,bool),X5),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X3)))),hAPP(fun(X2,fun(X5,bool)),fun(X5,fun(X2,bool)),combc(X2,X5,bool),hAPP(fun(X2,X5),fun(X2,fun(X5,bool)),hAPP(fun(X5,fun(X5,bool)),fun(fun(X2,X5),fun(X2,fun(X5,bool))),combb(X5,fun(X5,bool),X2),fequal(X5)),X6)))))),hAPP(fun(X2,bool),fun(X5,bool),hAPP(fun(X2,X5),fun(fun(X2,bool),fun(X5,bool)),image(X2,X5),X6),X3))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1539]),
    [final] ).

cnf(i_0_2785,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_7(X1,X2,X3,X4,X5,X6,X7)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk139_7(X1,X2,X3,X4,X5,X6,X7)),esk141_7(X1,X2,X3,X4,X5,X6,X7)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2786,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk142_7(X1,X2,X3,X4,X5,X6,X7)),X5))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X7),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X7),X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,esk138_7(X1,X2,X3,X4,X5,X6,X7)),esk140_7(X1,X2,X3,X4,X5,X6,X7)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),X6,X7),X7))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2787,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X3))),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X5)))) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X5))),X4)),zero_zero(X1))),X3)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1540]),
    [final] ).

cnf(i_0_2788,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(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),fconj),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(X3,fun(X1,bool),hAPP(fun(X1,fun(X3,bool)),fun(X3,fun(X1,bool)),combc(X1,X3,bool),hAPP(fun(X1,X3),fun(X1,fun(X3,bool)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X1,X3),fun(X1,fun(X3,bool))),combb(X3,fun(X3,bool),X1),fequal(X3)),X4)),hAPP(X1,X3,X4,esk117_4(X3,X1,X4,X2)))))))
    | ~ 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))) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_2789,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_1542]),
    [final] ).

cnf(i_0_2790,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X5)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X5))),X4)),zero_zero(X1))),X3)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1543]),
    [final] ).

cnf(i_0_2791,plain,
    ( hAPP(fun(X1,bool),X4,hAPP(fun(X1,X4),fun(fun(X1,bool),X4),big_co1399186613setsum(X1,X4),hAPP(X4,fun(X1,X4),hAPP(fun(X1,fun(X4,X4)),fun(X4,fun(X1,X4)),combc(X1,X4,X4),hAPP(fun(X1,X4),fun(X1,fun(X4,X4)),hAPP(fun(X1,fun(X4,fun(X4,X4))),fun(fun(X1,X4),fun(X1,fun(X4,X4))),combs(X1,X4,fun(X4,X4)),hAPP(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4))),hAPP(fun(bool,fun(X4,fun(X4,X4))),fun(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4)))),combb(bool,fun(X4,fun(X4,X4)),X1),if(X4)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),X5)),zero_zero(X4))),X3) = hAPP(X1,X4,X5,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ comm_monoid_add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_2792,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hAPP(fun(X1,bool),X4,hAPP(fun(X1,X4),fun(fun(X1,bool),X4),big_co1399186613setsum(X1,X4),hAPP(X4,fun(X1,X4),hAPP(fun(X1,fun(X4,X4)),fun(X4,fun(X1,X4)),combc(X1,X4,X4),hAPP(fun(X1,X4),fun(X1,fun(X4,X4)),hAPP(fun(X1,fun(X4,fun(X4,X4))),fun(fun(X1,X4),fun(X1,fun(X4,X4))),combs(X1,X4,fun(X4,X4)),hAPP(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4))),hAPP(fun(bool,fun(X4,fun(X4,X4))),fun(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4)))),combb(bool,fun(X4,fun(X4,X4)),X1),if(X4)),hAPP(X1,fun(X1,bool),hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combc(X1,X1,bool),fequal(X1)),X2))),X5)),zero_zero(X4))),X3) = zero_zero(X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ comm_monoid_add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_2793,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(bool,bool)),fun(fun(X2,bool),fun(X2,bool)),combs(X2,bool,bool),hAPP(fun(X2,bool),fun(X2,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X2,bool),fun(X2,fun(bool,bool))),combb(bool,fun(bool,bool),X2),fconj),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,fun(fun(X2,bool),bool)),fun(fun(X2,bool),fun(X2,bool)),combc(X2,fun(X2,bool),bool),member(X2)),X3))),X5))) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X2,fun(X1,fun(X1,X1))),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combs(X2,X1,fun(X1,X1)),hAPP(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1))),hAPP(fun(bool,fun(X1,fun(X1,X1))),fun(fun(X2,bool),fun(X2,fun(X1,fun(X1,X1)))),combb(bool,fun(X1,fun(X1,X1)),X2),if(X1)),X5)),X4)),zero_zero(X1))),X3)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_2794,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,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X1,fun(X2,fun(X2,X2))),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combs(X1,X2,fun(X2,X2)),hAPP(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2))),hAPP(fun(bool,fun(X2,fun(X2,X2))),fun(fun(X1,bool),fun(X1,fun(X2,fun(X2,X2)))),combb(bool,fun(X2,fun(X2,X2)),X1),if(X2)),X3)),X4)),X5)),X6) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X6),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),X3))))),
    inference(split_conjunct,[status(thm)],[i_0_1546]),
    [final] ).

cnf(i_0_2795,plain,
    ( hAPP(fun(X1,bool),X4,hAPP(fun(X1,X4),fun(fun(X1,bool),X4),big_co1399186613setsum(X1,X4),hAPP(X4,fun(X1,X4),hAPP(fun(X1,fun(X4,X4)),fun(X4,fun(X1,X4)),combc(X1,X4,X4),hAPP(fun(X1,X4),fun(X1,fun(X4,X4)),hAPP(fun(X1,fun(X4,fun(X4,X4))),fun(fun(X1,X4),fun(X1,fun(X4,X4))),combs(X1,X4,fun(X4,X4)),hAPP(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4))),hAPP(fun(bool,fun(X4,fun(X4,X4))),fun(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4)))),combb(bool,fun(X4,fun(X4,X4)),X1),if(X4)),hAPP(X1,fun(X1,bool),fequal(X1),X2))),X5)),zero_zero(X4))),X3) = hAPP(X1,X4,X5,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ comm_monoid_add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_2796,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hAPP(fun(X1,bool),X4,hAPP(fun(X1,X4),fun(fun(X1,bool),X4),big_co1399186613setsum(X1,X4),hAPP(X4,fun(X1,X4),hAPP(fun(X1,fun(X4,X4)),fun(X4,fun(X1,X4)),combc(X1,X4,X4),hAPP(fun(X1,X4),fun(X1,fun(X4,X4)),hAPP(fun(X1,fun(X4,fun(X4,X4))),fun(fun(X1,X4),fun(X1,fun(X4,X4))),combs(X1,X4,fun(X4,X4)),hAPP(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4))),hAPP(fun(bool,fun(X4,fun(X4,X4))),fun(fun(X1,bool),fun(X1,fun(X4,fun(X4,X4)))),combb(bool,fun(X4,fun(X4,X4)),X1),if(X4)),hAPP(X1,fun(X1,bool),fequal(X1),X2))),X5)),zero_zero(X4))),X3) = zero_zero(X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ comm_monoid_add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1547]),
    [final] ).

cnf(i_0_2797,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,esk47_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk46_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_1548]),
    [final] ).

cnf(i_0_2798,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,esk45_6(X2,X1,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk44_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_1549]),
    [final] ).

cnf(i_0_2799,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,esk52_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk53_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_1550]),
    [final] ).

cnf(i_0_2800,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,esk54_6(X2,X1,X3,X4,X5,X6))),hAPP(X2,X1,X3,esk55_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_1551]),
    [final] ).

cnf(i_0_2801,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,esk42_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk41_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_1552]),
    [final] ).

cnf(i_0_2802,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,esk40_6(X1,X2,X4,X3,X5,X6))),hAPP(X2,X1,X3,esk39_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_1553]),
    [final] ).

cnf(i_0_2803,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,esk50_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk51_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_1554]),
    [final] ).

cnf(i_0_2804,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,esk48_6(X1,X2,X4,X5,X3,X6))),hAPP(X2,X1,X3,esk49_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_1555]),
    [final] ).

cnf(i_0_2805,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1556,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2806,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1557,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2807,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X6)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X6)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1558,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2808,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1559,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2809,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1560,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2810,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1561,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2811,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk1_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1562,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2812,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X6)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X6)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk2_6(X4,X3,X5,X6,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X6)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1563,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2813,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X3,X6,X1,X2,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1564,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2814,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X6,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk4_6(X6,X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X5)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X6),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1565,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2815,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_1566]),
    [final] ).

cnf(i_0_2816,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2817,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X4)),X5)),one_one(X1)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3))
    | ~ comm_monoid_mult(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1568]),
    [final] ).

cnf(i_0_2818,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X3,bool),fun(X2,X1),hAPP(fun(X2,fun(fun(X3,bool),X1)),fun(fun(X3,bool),fun(X2,X1)),combc(X2,fun(X3,bool),X1),hAPP(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1)),hAPP(fun(fun(X3,X1),fun(fun(X3,bool),X1)),fun(fun(X2,fun(X3,X1)),fun(X2,fun(fun(X3,bool),X1))),combb(fun(X3,X1),fun(fun(X3,bool),X1),X2),big_co1399186613setsum(X3,X1)),X4)),X5)),X6) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X2,bool),fun(X3,X1),hAPP(fun(X3,fun(fun(X2,bool),X1)),fun(fun(X2,bool),fun(X3,X1)),combc(X3,fun(X2,bool),X1),hAPP(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1)),hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X3,fun(X2,X1)),fun(X3,fun(fun(X2,bool),X1))),combb(fun(X2,X1),fun(fun(X2,bool),X1),X3),big_co1399186613setsum(X2,X1)),hAPP(fun(X2,fun(X3,X1)),fun(X3,fun(X2,X1)),combc(X2,X3,X1),X4))),X6)),X5)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1569]),
    [final] ).

cnf(i_0_2819,plain,
    ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X1,X2)),esk26_2(X1,X2))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk24_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1193]),
    [final] ).

cnf(i_0_2820,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2821,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2822,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2823,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2824,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X3)),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))),hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X5),one_one(X1)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4)))
    | ~ comm_monoid_mult(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_2825,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk25_2(X1,X2)),esk26_2(X1,X2))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk24_2(X1,X2),X1)))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1193]),
    [final] ).

cnf(i_0_2826,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk24_2(X1,X2)),arrow_301600364e_Prof))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X2),X1))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1193]),
    [final] ).

cnf(i_0_2827,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2828,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2829,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1573,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2830,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1574,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2831,plain,
    ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X2),X1))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),esk26_2(X1,X2)) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),esk25_2(X1,X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1575,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2832,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2833,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2834,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_1576]),
    [final] ).

cnf(i_0_2835,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_1576]),
    [final] ).

cnf(i_0_2836,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2837,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2838,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2839,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2840,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2841,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_2842,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2843,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk9_5(X3,X4,X5,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk9_5(X3,X4,X5,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2844,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk9_5(X3,X5,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk9_5(X3,X5,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2845,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1578,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2846,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X5,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk3_5(X3,X5,X2,X4,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X5),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_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_1579,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2847,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1580,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2848,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1581,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2849,plain,
    ( hAPP(fun(X1,X6),fun(X1,X9),hAPP(fun(X6,X9),fun(fun(X1,X6),fun(X1,X9)),hAPP(fun(X1,bool),fun(fun(X6,X9),fun(fun(X1,X6),fun(X1,X9))),compose(X1,X6,X9),X4),X10),hAPP(fun(X1,X2),fun(X1,X6),hAPP(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6)),hAPP(fun(X1,bool),fun(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6))),compose(X1,X2,X6),X4),X7),X3)) = hAPP(fun(X1,X2),fun(X1,X9),hAPP(fun(X2,X9),fun(fun(X1,X2),fun(X1,X9)),hAPP(fun(X1,bool),fun(fun(X2,X9),fun(fun(X1,X2),fun(X1,X9))),compose(X1,X2,X9),X4),hAPP(fun(X2,X6),fun(X2,X9),hAPP(fun(X6,X9),fun(fun(X2,X6),fun(X2,X9)),hAPP(fun(X2,bool),fun(fun(X6,X9),fun(fun(X2,X6),fun(X2,X9))),compose(X2,X6,X9),X5),X10),X7)),X3)
    | ~ 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(fun(X2,X6),bool),bool,hAPP(fun(X2,X6),fun(fun(fun(X2,X6),bool),bool),member(fun(X2,X6)),X7),hAPP(fun(X2,fun(X6,bool)),fun(fun(X2,X6),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X6,bool)),fun(fun(X2,X6),bool)),pi(X2,X6),X5),hAPP(fun(X6,bool),fun(X2,fun(X6,bool)),combk(fun(X6,bool),X2),X8))))
    | ~ hBOOL(hAPP(fun(fun(X6,X9),bool),bool,hAPP(fun(X6,X9),fun(fun(fun(X6,X9),bool),bool),member(fun(X6,X9)),X10),hAPP(fun(X6,fun(X9,bool)),fun(fun(X6,X9),bool),hAPP(fun(X6,bool),fun(fun(X6,fun(X9,bool)),fun(fun(X6,X9),bool)),pi(X6,X9),X8),hAPP(fun(X9,bool),fun(X6,fun(X9,bool)),combk(fun(X9,bool),X6),X11)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_2850,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk52_6(X1,X2,X3,X4,X5,X6)),esk53_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_1550]),
    [final] ).

cnf(i_0_2851,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk54_6(X1,X2,X3,X4,X5,X6)),esk55_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_1551]),
    [final] ).

cnf(i_0_2852,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk47_6(X1,X2,X3,X4,X5,X6)),esk46_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_1548]),
    [final] ).

cnf(i_0_2853,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk45_6(X1,X2,X3,X4,X5,X6)),esk44_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_1549]),
    [final] ).

cnf(i_0_2854,plain,
    ( hBOOL(hAPP(fun(fun(X1,X6),bool),bool,hAPP(fun(X1,X6),fun(fun(fun(X1,X6),bool),bool),member(fun(X1,X6)),hAPP(fun(X1,X2),fun(X1,X6),hAPP(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6)),hAPP(fun(X1,bool),fun(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6))),compose(X1,X2,X6),X4),X7),X3)),hAPP(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X6,bool)),fun(fun(X1,X6),bool)),pi(X1,X6),X4),hAPP(fun(X6,bool),fun(X1,fun(X6,bool)),combk(fun(X6,bool),X1),X8))))
    | ~ 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(fun(X2,X6),bool),bool,hAPP(fun(X2,X6),fun(fun(fun(X2,X6),bool),bool),member(fun(X2,X6)),X7),hAPP(fun(X2,fun(X6,bool)),fun(fun(X2,X6),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X6,bool)),fun(fun(X2,X6),bool)),pi(X2,X6),X5),hAPP(fun(X6,bool),fun(X2,fun(X6,bool)),combk(fun(X6,bool),X2),X8)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_2855,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk173_5(X1,X2,X3,X4,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X5),X4)))
    | hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1584]),
    [final] ).

cnf(i_0_2856,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_1585]),
    [final] ).

cnf(i_0_2857,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk42_6(X2,X1,X3,X4,X5,X6)),esk41_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_1552]),
    [final] ).

cnf(i_0_2858,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk40_6(X2,X1,X3,X4,X5,X6)),esk39_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_1553]),
    [final] ).

cnf(i_0_2859,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk50_6(X2,X1,X3,X4,X5,X6)),esk51_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_1554]),
    [final] ).

cnf(i_0_2860,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk48_6(X2,X1,X3,X4,X5,X6)),esk49_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_1555]),
    [final] ).

cnf(i_0_2861,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2862,plain,
    ( hAPP(X2,X4,hAPP(fun(X4,X2),fun(X2,X4),hAPP(fun(X4,bool),fun(fun(X4,X2),fun(X2,X4)),hilbert_inv_into(X4,X2),X6),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X7) = hAPP(X2,X4,hAPP(fun(X2,X1),fun(X2,X4),hAPP(fun(X1,X4),fun(fun(X2,X1),fun(X2,X4)),comp(X1,X4,X2),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)),X3)),X7)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
    | ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),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)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_2863,plain,
    ( hAPP(X2,X4,hAPP(fun(X4,X2),fun(X2,X4),hAPP(fun(X4,bool),fun(fun(X4,X2),fun(X2,X4)),the_inv_into(X4,X2),X6),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X7) = hAPP(X2,X4,hAPP(fun(X2,X1),fun(X2,X4),hAPP(fun(X1,X4),fun(fun(X2,X1),fun(X2,X4)),comp(X1,X4,X2),hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),the_inv_into(X4,X1),X6),X5)),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)),X3)),X7)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
    | ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X7),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)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1587]),
    [final] ).

cnf(i_0_2864,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2865,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1588,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2866,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1589,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2867,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2868,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_2869,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_2870,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X3,X4,X2,X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1592,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2871,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X4),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1593,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2872,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2873,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,esk59_5(X1,X2,X3,X4,X5))),hAPP(X2,fun(X1,bool),X4,esk59_5(X1,X2,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1594]),
    [final] ).

cnf(i_0_2874,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2875,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2876,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
    inference(rw,[status(thm)],[i_0_1595,c_0_1517]),
    [final] ).

cnf(i_0_2877,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | ~ linord581940658strict(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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))),zero_zero(X1))) ),
    inference(rw,[status(thm)],[i_0_1596,c_0_1517]),
    [final] ).

cnf(i_0_2878,plain,
    ( ~ linordered_ring(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),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1597]),
    [final] ).

cnf(i_0_2879,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_1598]),
    [final] ).

cnf(i_0_2880,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_1598]),
    [final] ).

cnf(i_0_2881,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2882,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1599]),
    [final] ).

cnf(i_0_2883,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(X2,X1),X3),X5)),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,esk132_5(X1,X2,X3,X4,X5))),hAPP(X2,fun(X1,bool),X4,esk132_5(X1,X2,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1600]),
    [final] ).

cnf(i_0_2884,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X4)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),times_times(X2),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X5)),hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4))
    | hAPP(X1,X2,X3,esk173_5(X1,X2,X3,X4,X5)) != one_one(X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1584]),
    [final] ).

cnf(i_0_2885,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),esk22_4(X1,X2,X3,X4)),esk23_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),esk22_4(X1,X2,X3,X4)),esk23_4(X1,X2,X3,X4))),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1601,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2886,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_1576]),
    [final] ).

cnf(i_0_2887,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_301600364e_Prof),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1568854078le_Lin)))),
    inference(split_conjunct,[status(thm)],[fact_32_assms_I1_J]),
    [final] ).

cnf(i_0_2888,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2889,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2890,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2891,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk137_6(X1,X2,X3,X4,X5,X6)),X6))
    | hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X4),X3),X6) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X5),X3),X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
    | ~ ab_semigroup_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2892,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_1603]),
    [final] ).

cnf(i_0_2893,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_1603]),
    [final] ).

cnf(i_0_2894,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),esk75_2(X1,X2)),hAPP(nat,nat,X2,esk75_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1604]),
    [final] ).

cnf(i_0_2895,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e))) ),
    inference(cn,[status(thm)],[i_0_1605]),
    [final] ).

cnf(i_0_2896,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X1,fun(X2,X2)),fun(fun(X1,X2),fun(X1,X2)),combs(X1,X2,X2),hAPP(fun(X1,X2),fun(X1,fun(X2,X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X1,fun(X2,X2))),combb(X2,fun(X2,X2),X1),X3),X7)),X8)),X6) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6)),hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1606]),
    [final] ).

cnf(i_0_2897,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2898,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X3)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1607,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2899,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X1)),X5))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1608,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2900,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1609,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2901,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1610,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2902,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1611,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2903,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1612,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2904,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X5),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1613,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2905,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1614,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2906,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_1615]),
    [final] ).

cnf(i_0_2907,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_1616]),
    [final] ).

cnf(i_0_2908,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_1598]),
    [final] ).

cnf(i_0_2909,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_1598]),
    [final] ).

cnf(i_0_2910,plain,
    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),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X4),X5))),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)))),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2911,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(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)),X5)),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))))
    | 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(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X5) ),
    inference(rw,[status(thm)],[i_0_1618,c_0_1517]),
    [final] ).

cnf(i_0_2912,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2913,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_1619]),
    [final] ).

cnf(i_0_2914,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X4))),X3))
    | ~ linord1278240602ring_1(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),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),X6) != one_one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1620]),
    [final] ).

cnf(i_0_2915,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),times_times(X1),X5),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X4))),X3))
    | ~ linord626643107strict(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),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X5),X6) != one_one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1621]),
    [final] ).

cnf(i_0_2916,plain,
    ( hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(X2,X1),X3),X5)),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,esk133_5(X1,X2,X3,X4,X5))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1622]),
    [final] ).

cnf(i_0_2917,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),X4),X6) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X5),X4),X6)
    | hAPP(X1,X2,X3,esk137_6(X1,X2,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk137_6(X1,X2,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
    | ~ ab_semigroup_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2918,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2919,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1623]),
    [final] ).

cnf(i_0_2920,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_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_1624,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2921,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X3)),X5))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_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_1625,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2922,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2923,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2924,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_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_1626,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2925,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_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_1627,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2926,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(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)),X3)),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)),X4)),X2))
    | ~ 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1590]),
    [final] ).

cnf(i_0_2927,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(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)),X3)),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)),X4)),X2))
    | ~ 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1591]),
    [final] ).

cnf(i_0_2928,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X3),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1628,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2929,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),X5))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1629,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2930,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2931,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2932,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1194]),
    [final] ).

cnf(i_0_2933,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2934,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_2935,plain,
    ( 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),X4),X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk147_6(X2,X1,X3,X4,X5,X6)),X6))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X6) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1631,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2936,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2937,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba))
    | hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2938,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2939,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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),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_1632]),
    [final] ).

cnf(i_0_2940,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = 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),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_1633]),
    [final] ).

cnf(i_0_2941,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X5))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X5))))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1634]),
    [final] ).

cnf(i_0_2942,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2943,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_1635]),
    [final] ).

cnf(i_0_2944,plain,
    ( hAPP(fun(X1,bool),X2,X6,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X7),X8)) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),X3,hAPP(fun(X1,bool),X2,X6,X7)),hAPP(fun(X1,bool),X2,X6,X8))
    | ~ 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,finite_finite_1(X1),X8)) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_2945,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_1637]),
    [final] ).

cnf(i_0_2946,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_1638]),
    [final] ).

cnf(i_0_2947,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1639,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2948,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1640,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2949,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1641,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2950,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X3)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1642,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2951,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1643,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2952,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X5),X4)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1644,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2953,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_1645]),
    [final] ).

cnf(i_0_2954,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1646,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2955,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X5),X4)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1647,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2956,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
    | hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1648,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2957,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X3),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1649,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2958,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_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_1650,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2959,plain,
    ( 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),X5)),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,esk131_5(X1,X2,X3,X4,X5))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_2960,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2961,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2962,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_1652]),
    [final] ).

cnf(i_0_2963,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),esk22_4(X1,X2,X3,X4)),esk23_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),esk22_4(X1,X2,X3,X4)),esk23_4(X1,X2,X3,X4))),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1653,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2964,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2965,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X4),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1654,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2966,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X5)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X4),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1655,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2967,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),e)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_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_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2968,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X2),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X4)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X2,esk14_4(X1,X2,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_2969,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e))) ),
    inference(cn,[status(thm)],[i_0_1657]),
    [final] ).

cnf(i_0_2970,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X4) = hAPP(fun(X2,bool),nat,finite_card(X2),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,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(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X6),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),X6),X5)),X4))
    | ~ 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_1658]),
    [final] ).

cnf(i_0_2971,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1659]),
    [final] ).

cnf(i_0_2972,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_1660,c_0_1517]),
    [final] ).

cnf(i_0_2973,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),plus_plus(X1)),X4)),X5)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X3)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),X3))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1661]),
    [final] ).

cnf(i_0_2974,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2975,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(fun(X2,X1),fun(X2,X1)),combs(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),plus_plus(X1)),X3)),X4)),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X5)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X5))
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1662]),
    [final] ).

cnf(i_0_2976,plain,
    ( 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),X4),X6)
    | hAPP(X1,X2,X3,esk147_6(X2,X1,X3,X4,X5,X6)) != hAPP(X1,X2,X4,esk147_6(X2,X1,X3,X4,X5,X6))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X6) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1663,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2977,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5))
    | hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) != hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5)))
    | hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_2978,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1570]),
    [final] ).

cnf(i_0_2979,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)) ),
    inference(cn,[status(thm)],[i_0_1665]),
    [final] ).

cnf(i_0_2980,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X2),X5)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_2981,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X3),X4)),X5) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),hAPP(fun(X2,fun(X1,X1)),fun(X1,fun(X2,X1)),combc(X2,X1,X1),hAPP(fun(X2,X1),fun(X2,fun(X1,X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X2,fun(X1,X1))),combb(X1,fun(X1,X1),X2),times_times(X1)),X3)),X5)),X4)
    | ~ semiring_0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1667]),
    [final] ).

cnf(i_0_2982,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_1619]),
    [final] ).

cnf(i_0_2983,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1668,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2984,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1669,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2985,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_1670]),
    [final] ).

cnf(i_0_2986,plain,
    ( hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ linord581940658strict(X1)
    | ~ 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1671,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2987,plain,
    ( hAPP(arrow_1998540521e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1998540521e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),e),d)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)) ),
    inference(cn,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_2988,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X4))
    | hAPP(X1,X2,X3,hAPP(X1,X1,X5,esk124_5(X2,X1,X3,X5,X4))) != hAPP(X1,X2,X3,hAPP(X1,X1,X5,esk125_5(X2,X1,X3,X5,X4)))
    | hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X5,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_2989,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X4),X3),X5)),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(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),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,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_2990,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2991,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1674,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_2992,plain,
    ( hBOOL(hAPP(X1,bool,X2,X5))
    | ~ hBOOL(hAPP(X1,bool,X2,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),top_top(fun(X1,bool))),X4),esk108_5(X1,X3,X5,X2,X4))))
    | ~ 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(split_conjunct,[status(thm)],[i_0_1675]),
    [final] ).

cnf(i_0_2993,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),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_2994,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),times_times(nat),hAPP(nat,nat,suc,X1)),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_2995,plain,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_2996,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_1679]),
    [final] ).

cnf(i_0_2997,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X8),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X7),X6)) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),comp(X1,X2,X1),X8),X7)),X6)
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X7),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_2998,plain,
    hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2))),compose(X1,X3,X2),X4),X5),X6)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
    inference(split_conjunct,[status(thm)],[i_0_1681]),
    [final] ).

cnf(i_0_2999,plain,
    ( hAPP(fun(X1,X2),fun(X1,X2),hAPP(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X2,X2),fun(fun(X1,X2),fun(X1,X2))),compose(X1,X2,X2),X4),hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X5)),X3) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
    inference(rw,[status(thm)],[i_0_1682,c_0_1517]),
    [final] ).

cnf(i_0_3000,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_1683]),
    [final] ).

cnf(i_0_3001,plain,
    ( hAPP(fun(X4,bool),X1,hAPP(X1,fun(fun(X4,bool),X1),hAPP(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X4,X1),fun(X1,fun(fun(X4,bool),X1))),finite_fold_image(X1,X4),times_times(X1)),X6),X7),hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X5),X3)) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),hAPP(fun(X2,X4),fun(X2,X1),hAPP(fun(X4,X1),fun(fun(X2,X4),fun(X2,X1)),comp(X4,X1,X2),X6),X5)),X7),X3)
    | ~ ab_semigroup_mult(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X4),fun(fun(X2,bool),bool),inj_on(X2,X4),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1684]),
    [final] ).

cnf(i_0_3002,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk59_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_1594]),
    [final] ).

cnf(i_0_3003,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1685,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3004,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1686,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3005,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X5),X2),X4)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_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_1687,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3006,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X5),X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X5),arrow_1568854078le_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_1688,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3007,plain,
    ( 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(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3008,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X5,X7),X6) = hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),X3),X7),X4),X6)
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1690]),
    [final] ).

cnf(i_0_3009,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk133_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X5)),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_1622]),
    [final] ).

cnf(i_0_3010,plain,
    ( hAPP(fun(X1,X1),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2)),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(fun(X1,X1),fun(X1,X2))),compose(X1,X1,X2),X4),X3),hAPP(fun(X1,bool),fun(X1,X1),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,X1)),restrict(X1,X1),combi(X1)),X4)) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
    inference(rw,[status(thm)],[i_0_1691,c_0_1517]),
    [final] ).

cnf(i_0_3011,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_1692]),
    [final] ).

cnf(i_0_3012,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_1693]),
    [final] ).

cnf(i_0_3013,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk124_5(X2,X1,X3,X4,X5))) = hAPP(X1,X2,X3,hAPP(X1,X1,X4,esk125_5(X2,X1,X3,X4,X5)))
    | hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X4,X5)) = hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3014,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X3),X2)),finite_psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3015,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),p,hAPP(nat,arrow_1998540521e_indi,hAPP(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,nat),fun(nat,arrow_1998540521e_indi)),hilbert_inv_into(arrow_1998540521e_indi,nat),top_top(fun(arrow_1998540521e_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_3016,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_1694]),
    [final] ).

cnf(i_0_3017,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1695,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3018,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1696,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3019,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1697,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3020,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X4)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1698,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3021,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_1699]),
    [final] ).

cnf(i_0_3022,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3023,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk10_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk11_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3024,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1700]),
    [final] ).

cnf(i_0_3025,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_1701]),
    [final] ).

cnf(i_0_3026,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk132_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)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X5)),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_1600]),
    [final] ).

cnf(i_0_3027,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,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_eq(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1702]),
    [final] ).

cnf(i_0_3028,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,esk92_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk92_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_1703]),
    [final] ).

cnf(i_0_3029,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_1694]),
    [final] ).

cnf(i_0_3030,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X5))
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_3031,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X5),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X5))
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1705]),
    [final] ).

cnf(i_0_3032,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(fun(X2,bool)),X3),X4))),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(fun(X2,bool)),X3),X4))) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),X3)),hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),X4))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1706]),
    [final] ).

cnf(i_0_3033,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1707]),
    [final] ).

cnf(i_0_3034,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X4)))
    | hAPP(X1,X2,X3,hAPP(X1,X1,X5,esk124_5(X2,X1,X3,X5,X4))) = hAPP(X1,X2,X3,hAPP(X1,X1,X5,esk125_5(X2,X1,X3,X5,X4)))
    | hAPP(X1,X2,X3,esk124_5(X2,X1,X3,X5,X4)) = hAPP(X1,X2,X3,esk125_5(X2,X1,X3,X5,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,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3035,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)),X5)
    | ~ semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_3036,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_1709]),
    [final] ).

cnf(i_0_3037,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_1710,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3038,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_1711,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3039,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_3040,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X6),X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_3041,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1713]),
    [final] ).

cnf(i_0_3042,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X4,X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1714]),
    [final] ).

cnf(i_0_3043,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_1715]),
    [final] ).

cnf(i_0_3044,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_1716,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3045,plain,
    ( 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),esk107_4(X1,X2,X3,X4)),X4)),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X2,bool),nat,finite_card(X2),X4)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1717]),
    [final] ).

cnf(i_0_3046,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_1718]),
    [final] ).

cnf(i_0_3047,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(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ 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(X2,bool),bool,finite_finite_1(X2),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1717]),
    [final] ).

cnf(i_0_3048,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(X1,fun(fun(X1,bool),bool),member(X1),esk125_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3049,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(X1,fun(fun(X1,bool),bool),member(X1),esk124_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3050,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),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3051,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(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ 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(X2,bool),bool,finite_finite_1(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1720]),
    [final] ).

cnf(i_0_3052,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_1721]),
    [final] ).

cnf(i_0_3053,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X2),fun(fun(X3,bool),bool),inj_on(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),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1722]),
    [final] ).

cnf(i_0_3054,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X3))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1723,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3055,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_1724]),
    [final] ).

cnf(i_0_3056,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),hAPP(fun(X1,X2),fun(X1,X5),hAPP(fun(X2,X5),fun(fun(X1,X2),fun(X1,X5)),comp(X2,X5,X1),X6),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(X2,bool),bool,hAPP(fun(X2,X5),fun(fun(X2,bool),bool),inj_on(X2,X5),X6),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1725]),
    [final] ).

cnf(i_0_3057,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(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)))
    | ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1707]),
    [final] ).

cnf(i_0_3058,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_1679]),
    [final] ).

cnf(i_0_3059,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)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk145_5(X1,X2,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)),X4),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1726,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3060,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk10_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3061,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X5),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3))),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X5),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X5),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X4))
    | ~ comm_monoid_add(X1)
    | ~ 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),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_3062,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_1693]),
    [final] ).

cnf(i_0_3063,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_3064,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X3)),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3065,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),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_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3066,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),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_gr676655987ssThan(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3067,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),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_gr676655987ssThan(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3068,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),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_gr1471790799AtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3069,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),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_gr1471790799AtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3070,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),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),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3071,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),X4),X2))
    | ~ 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_gr676655987ssThan(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3072,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),X4),X2))
    | ~ 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_gr676655987ssThan(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3073,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),X4),X2))
    | ~ 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_gr1471790799AtMost(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3074,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),X4),X2))
    | ~ 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_atLeastAtMost(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3075,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),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_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3076,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),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3077,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),X2))
    | ~ 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_atLeastAtMost(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X5),X3)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3078,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),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X5),X3)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3079,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),X4),X2))
    | ~ 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_atLeastAtMost(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3080,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),X4),X2))
    | ~ 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_gr1471790799AtMost(X1),X4),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X3)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3081,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1735,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3082,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1736,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3083,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[i_0_1737,c_0_1517]),
    [final] ).

cnf(i_0_3084,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | 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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[i_0_1738,c_0_1517]),
    [final] ).

cnf(i_0_3085,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X4)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk125_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))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3086,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X5),X4)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk124_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))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1664]),
    [final] ).

cnf(i_0_3087,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
    | ~ linordered_ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_3088,plain,
    ( hBOOL(hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool,hAPP(product_prod(fun(X1,bool),fun(X1,bool)),fun(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),bool),member(product_prod(fun(X1,bool),fun(X1,bool))),hAPP(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),product_prod(fun(X1,bool),fun(X1,bool))),product_Pair(fun(X1,bool),fun(X1,bool)),X2),X3)),finite_psubset(X1)))
    | ~ 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,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1689]),
    [final] ).

cnf(i_0_3089,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool),hAPP(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)),mlex_prod(X1),X2),X5)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_3090,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_1637]),
    [final] ).

cnf(i_0_3091,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1741,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3092,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1742,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3093,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_1743]),
    [final] ).

cnf(i_0_3094,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_1743]),
    [final] ).

cnf(i_0_3095,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_1744]),
    [final] ).

cnf(i_0_3096,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),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_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X5))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3097,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X5),X2)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),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),X4),X5))
    | ~ 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))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3098,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X4,X2)),hAPP(X1,nat,X4,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X2),X3)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1745]),
    [final] ).

cnf(i_0_3099,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),esk111_5(X1,X2,X3,X4,X5)),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),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(X2,bool),bool,finite_finite_1(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1235]),
    [final] ).

cnf(i_0_3100,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_1746,c_0_1517]),
    [final] ).

cnf(i_0_3101,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X5)))
    | ~ 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)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1747]),
    [final] ).

cnf(i_0_3102,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X5)))
    | ~ 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)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1748]),
    [final] ).

cnf(i_0_3103,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk131_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)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_3104,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3105,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_1701]),
    [final] ).

cnf(i_0_3106,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_inf_inf(fun(X2,fun(X1,bool))),X3),X6),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1749]),
    [final] ).

cnf(i_0_3107,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_1750]),
    [final] ).

cnf(i_0_3108,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_1751]),
    [final] ).

cnf(i_0_3109,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_1239]),
    [final] ).

cnf(i_0_3110,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,esk145_5(X1,X2,X4,X3,X5)) != hAPP(X1,X2,X4,esk145_5(X1,X2,X4,X3,X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1752,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3111,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_1753]),
    [final] ).

cnf(i_0_3112,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_1754]),
    [final] ).

cnf(i_0_3113,plain,
    ( hAPP(fun(X1,bool),fun(X6,bool),hAPP(fun(X1,X6),fun(fun(X1,bool),fun(X6,bool)),image(X1,X6),hAPP(fun(X1,X2),fun(X1,X6),hAPP(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6)),hAPP(fun(X1,bool),fun(fun(X2,X6),fun(fun(X1,X2),fun(X1,X6))),compose(X1,X2,X6),X4),X7),X3)),X4) = hAPP(fun(X6,bool),fun(X6,bool),combi(fun(X6,bool)),X8)
    | hAPP(fun(X2,bool),fun(X6,bool),hAPP(fun(X2,X6),fun(fun(X2,bool),fun(X6,bool)),image(X2,X6),X7),X5) != hAPP(fun(X6,bool),fun(X6,bool),combi(fun(X6,bool)),X8)
    | 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(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X5) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1755,c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3114,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1756]),
    [final] ).

cnf(i_0_3115,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1757]),
    [final] ).

cnf(i_0_3116,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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1758]),
    [final] ).

cnf(i_0_3117,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ linordered_semiring(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1759]),
    [final] ).

cnf(i_0_3118,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1760]),
    [final] ).

cnf(i_0_3119,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ linordered_semiring(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1761]),
    [final] ).

cnf(i_0_3120,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_3121,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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1763]),
    [final] ).

cnf(i_0_3122,plain,
    ( 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_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1764]),
    [final] ).

cnf(i_0_3123,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1765]),
    [final] ).

cnf(i_0_3124,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5)),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1766]),
    [final] ).

cnf(i_0_3125,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(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))
    | ~ 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_1767]),
    [final] ).

cnf(i_0_3126,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk109_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_1243]),
    [final] ).

cnf(i_0_3127,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk103_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_1244]),
    [final] ).

cnf(i_0_3128,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ ordered_semiring(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))
    | ~ 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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1768]),
    [final] ).

cnf(i_0_3129,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ ordered_semiring(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))
    | ~ 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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1769]),
    [final] ).

cnf(i_0_3130,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ linord20386208strict(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))
    | ~ 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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_3131,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ linord20386208strict(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))
    | ~ 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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1771]),
    [final] ).

cnf(i_0_3132,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ linord20386208strict(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))
    | ~ 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)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_3133,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)))
    | ~ linord20386208strict(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))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_3134,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_1774]),
    [final] ).

cnf(i_0_3135,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1775]),
    [final] ).

cnf(i_0_3136,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1776]),
    [final] ).

cnf(i_0_3137,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_3138,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),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1778]),
    [final] ).

cnf(i_0_3139,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X5),X6)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1779]),
    [final] ).

cnf(i_0_3140,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),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3141,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),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3142,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),zero_zero(X1)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3143,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),zero_zero(X1)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3144,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),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3145,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),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3146,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))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3147,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))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3148,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_1782]),
    [final] ).

cnf(i_0_3149,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1783]),
    [final] ).

cnf(i_0_3150,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1784]),
    [final] ).

cnf(i_0_3151,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_1615]),
    [final] ).

cnf(i_0_3152,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_1616]),
    [final] ).

cnf(i_0_3153,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_1785]),
    [final] ).

cnf(i_0_3154,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),hAPP(nat,nat,suc,X1))) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X1))),hAPP(nat,X3,X4,hAPP(nat,nat,suc,X1)))
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1786]),
    [final] ).

cnf(i_0_3155,plain,
    ( hAPP(fun(X1,X2),fun(X1,X4),hAPP(fun(X2,X4),fun(fun(X1,X2),fun(X1,X4)),comp(X2,X4,X1),hAPP(fun(X2,X1),fun(X2,X4),hAPP(fun(X1,X4),fun(fun(X2,X1),fun(X2,X4)),comp(X1,X4,X2),X5),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))),X3) = hAPP(fun(X1,X4),fun(X1,X4),combi(fun(X1,X4)),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)],[i_0_1787,c_0_1517]),
    [final] ).

cnf(i_0_3156,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk108_5(X2,X1,X3,X4,X5)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X5),top_top(fun(X2,bool)))))
    | hBOOL(hAPP(X2,bool,X4,X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X5),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1675]),
    [final] ).

cnf(i_0_3157,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk15_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_3158,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X6),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1788]),
    [final] ).

cnf(i_0_3159,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X3),X6),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1789]),
    [final] ).

cnf(i_0_3160,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1790]),
    [final] ).

cnf(i_0_3161,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool)),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),fun(X2,fun(X1,bool))),semilattice_sup_sup(fun(X2,fun(X1,bool))),X6),X3),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1789]),
    [final] ).

cnf(i_0_3162,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1791]),
    [final] ).

cnf(i_0_3163,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X1),X2)),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1792]),
    [final] ).

cnf(i_0_3164,plain,
    ( 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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1793]),
    [final] ).

cnf(i_0_3165,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X2),fun(fun(X4,bool),bool),inj_on(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5)),top_top(fun(X4,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))))
    | ~ hBOOL(hAPP(fun(X4,bool),bool,hAPP(fun(X4,X1),fun(fun(X4,bool),bool),inj_on(X4,X1),X5),top_top(fun(X4,bool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1794]),
    [final] ).

cnf(i_0_3166,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_1795]),
    [final] ).

cnf(i_0_3167,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_1796]),
    [final] ).

cnf(i_0_3168,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_1797]),
    [final] ).

cnf(i_0_3169,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_1798]),
    [final] ).

cnf(i_0_3170,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_1799]),
    [final] ).

cnf(i_0_3171,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_1800]),
    [final] ).

cnf(i_0_3172,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_1801]),
    [final] ).

cnf(i_0_3173,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_1802]),
    [final] ).

cnf(i_0_3174,plain,
    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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1803]),
    [final] ).

cnf(i_0_3175,plain,
    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)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1804]),
    [final] ).

cnf(i_0_3176,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X1),bool),bool,hAPP(product_prod(X1,X1),fun(fun(product_prod(X1,X1),bool),bool),member(product_prod(X1,X1)),hAPP(X1,product_prod(X1,X1),hAPP(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X3),X4)),hAPP(fun(X1,nat),fun(product_prod(X1,X1),bool),measure(X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X1,nat,X2,X3)),hAPP(X1,nat,X2,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1745]),
    [final] ).

cnf(i_0_3177,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_1805]),
    [final] ).

cnf(i_0_3178,plain,
    ( hAPP(fun(X2,X1),fun(X2,X2),hAPP(fun(X1,X2),fun(fun(X2,X1),fun(X2,X2)),hAPP(fun(X2,bool),fun(fun(X1,X2),fun(fun(X2,X1),fun(X2,X2))),compose(X2,X1,X2),X5),X3),hAPP(fun(X2,bool),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X2,X1)),restrict(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)),X5)) = hAPP(fun(X2,bool),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,X2)),restrict(X2,X2),combi(X2)),X5)
    | 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(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X5) ),
    inference(rw,[status(thm)],[i_0_1806,c_0_1517]),
    [final] ).

cnf(i_0_3179,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X4),X3)),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)) ),
    inference(split_conjunct,[status(thm)],[i_0_1807]),
    [final] ).

cnf(i_0_3180,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1808]),
    [final] ).

cnf(i_0_3181,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),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1809]),
    [final] ).

cnf(i_0_3182,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_1810]),
    [final] ).

cnf(i_0_3183,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,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1809]),
    [final] ).

cnf(i_0_3184,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,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1808]),
    [final] ).

cnf(i_0_3185,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_1811]),
    [final] ).

cnf(i_0_3186,plain,
    ( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1812,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3187,plain,
    ( hAPP(X1,X1,combi(X1),X4) = hAPP(X1,X1,combi(X1),X5)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1813,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3188,plain,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_inv_into(X1,X2),X4),X3),X5)) = 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),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    inference(rw,[status(thm)],[i_0_1814,c_0_1517]),
    [final] ).

cnf(i_0_3189,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,esk43_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk43_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1815]),
    [final] ).

cnf(i_0_3190,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,esk30_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk30_4(X2,X1,X3,X4))))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1816]),
    [final] ).

cnf(i_0_3191,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X3,X4)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3192,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),X4),X3)),X6)) = hAPP(fun(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X6)
    | 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(X2,bool),fun(X2,bool),combi(fun(X2,bool)),X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X6),X5)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1818,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3193,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,bool,X2,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3194,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),c),d)),hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),f,p))),
    inference(split_conjunct,[status(thm)],[i_0_1820]),
    [final] ).

cnf(i_0_3195,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
    | ~ 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),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_1821]),
    [final] ).

cnf(i_0_3196,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_1774]),
    [final] ).

cnf(i_0_3197,plain,
    ( 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_gr676655987ssThan(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3198,plain,
    ( 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_gr676655987ssThan(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3199,plain,
    ( 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_gr1471790799AtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3200,plain,
    ( 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_gr1471790799AtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3201,plain,
    ( 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_atLeastAtMost(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3202,plain,
    ( 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_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5)))
    | ~ 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))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3203,plain,
    ( 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_atLeastAtMost(X1),X3),X4)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X5)))
    | ~ 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))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3204,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),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(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1822]),
    [final] ).

cnf(i_0_3205,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1823]),
    [final] ).

cnf(i_0_3206,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1824]),
    [final] ).

cnf(i_0_3207,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,suc,X1))) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X1))),hAPP(nat,X3,X4,X1))
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1825]),
    [final] ).

cnf(i_0_3208,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combk(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),arrow_1998540521e_indi),X1)),arrow_301600364e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X1),arrow_1568854078le_Lin)) ),
    inference(split_conjunct,[status(thm)],[i_0_1826]),
    [final] ).

cnf(i_0_3209,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1719]),
    [final] ).

cnf(i_0_3210,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),esk135_3(X1,X2,X3)),X2)),X3))
    | ~ linord1117847801e_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1827]),
    [final] ).

cnf(i_0_3211,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk171_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(X1,bool,X2,X5))
    | ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3212,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk170_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,bool,X2,X5))
    | ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3213,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) != hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_3214,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),esk79_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_1829]),
    [final] ).

cnf(i_0_3215,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),esk79_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_1829]),
    [final] ).

cnf(i_0_3216,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),esk111_5(X1,X2,X3,X4,X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),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(X2,bool),bool,finite_finite_1(X2),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1235]),
    [final] ).

cnf(i_0_3217,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_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_1830,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3218,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X4),X2)))
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) != hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_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_1831,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3219,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X4,X2)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X2)),X3)))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1832]),
    [final] ).

cnf(i_0_3220,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X4,X2)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X2)),X3)))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1833]),
    [final] ).

cnf(i_0_3221,plain,
    ( hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,X3) = hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X3,X2)
    | ~ hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),X3),arrow_301600364e_Prof)) ),
    inference(split_conjunct,[status(thm)],[i_0_1834]),
    [final] ).

cnf(i_0_3222,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
    | ~ ordered_semiring(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1835]),
    [final] ).

cnf(i_0_3223,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ ordere1490568538miring(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1836]),
    [final] ).

cnf(i_0_3224,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ ordered_semiring(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1837]),
    [final] ).

cnf(i_0_3225,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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(X1),zero_zero(X1)),X4))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1758]),
    [final] ).

cnf(i_0_3226,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ 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))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3227,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
    | ~ linord20386208strict(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1838]),
    [final] ).

cnf(i_0_3228,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ 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))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3229,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ linord893533164strict(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1839]),
    [final] ).

cnf(i_0_3230,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
    | ~ linord20386208strict(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),zero_zero(X1)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1840]),
    [final] ).

cnf(i_0_3231,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),zero_zero(X1)),X4))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1763]),
    [final] ).

cnf(i_0_3232,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ ordered_ring(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1841]),
    [final] ).

cnf(i_0_3233,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ ordered_ring(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1842]),
    [final] ).

cnf(i_0_3234,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ 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),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1764]),
    [final] ).

cnf(i_0_3235,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ 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),X4))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_3236,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
    | ~ linord581940658strict(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1843]),
    [final] ).

cnf(i_0_3237,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
    | ~ 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),X4))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1781]),
    [final] ).

cnf(i_0_3238,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)))
    | ~ linord581940658strict(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1844]),
    [final] ).

cnf(i_0_3239,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),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),X4),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1765]),
    [final] ).

cnf(i_0_3240,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk166_4(X1,X2,X3,X4)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3241,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk167_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3242,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X5)))
    | ~ semilattice_sup(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_1845]),
    [final] ).

cnf(i_0_3243,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X5)))
    | ~ semilattice_inf(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_1846]),
    [final] ).

cnf(i_0_3244,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_1847]),
    [final] ).

cnf(i_0_3245,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_1848]),
    [final] ).

cnf(i_0_3246,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_1849]),
    [final] ).

cnf(i_0_3247,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_1850]),
    [final] ).

cnf(i_0_3248,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_1851]),
    [final] ).

cnf(i_0_3249,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)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3250,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),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3251,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),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),times_times(X1),X3),X2)),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3252,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),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3253,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),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(nat),zero_zero(nat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1776]),
    [final] ).

cnf(i_0_3254,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)))
    | ~ 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),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1808]),
    [final] ).

cnf(i_0_3255,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),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),zero_zero(nat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1853]),
    [final] ).

cnf(i_0_3256,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)))
    | ~ 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),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1809]),
    [final] ).

cnf(i_0_3257,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),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),zero_zero(nat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1778]),
    [final] ).

cnf(i_0_3258,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),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),zero_zero(nat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1854]),
    [final] ).

cnf(i_0_3259,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1855]),
    [final] ).

cnf(i_0_3260,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_1856]),
    [final] ).

cnf(i_0_3261,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_1857]),
    [final] ).

cnf(i_0_3262,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1858]),
    [final] ).

cnf(i_0_3263,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1859]),
    [final] ).

cnf(i_0_3264,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1860]),
    [final] ).

cnf(i_0_3265,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X2))
    | ~ linordered_idom(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))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1861]),
    [final] ).

cnf(i_0_3266,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),X2))
    | ~ linordered_idom(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))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),one_one(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1862]),
    [final] ).

cnf(i_0_3267,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_1863,c_0_1517]),
    [final] ).

cnf(i_0_3268,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_1754]),
    [final] ).

cnf(i_0_3269,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_1864,c_0_1517]),
    [final] ).

cnf(i_0_3270,plain,
    ( hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk154_1(X1)),X2)) = hAPP(nat,nat,X1,esk154_1(X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,hAPP(nat,nat,suc,esk153_1(X1)))),hAPP(nat,nat,X1,esk153_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1865]),
    [final] ).

cnf(i_0_3271,plain,
    ( hBOOL(hAPP(X1,bool,X2,X5))
    | ~ hBOOL(hAPP(X1,bool,X2,esk171_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X1,bool,X2,esk170_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3272,plain,
    ( hAPP(X3,X3,combi(X3),X5) = hAPP(X3,X3,combi(X3),esk104_4(X3,X1,X2,X4))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X3,X1,X4,X5)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool))))
    | ~ 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))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1866,c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3273,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lab)),
    inference(split_conjunct,[status(thm)],[i_0_1867]),
    [final] ).

cnf(i_0_3274,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lba)),
    inference(split_conjunct,[status(thm)],[i_0_1868]),
    [final] ).

cnf(i_0_3275,plain,
    ( 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),top_top(fun(X1,bool)))))
    | hAPP(X2,X2,combi(X2),X3) != hAPP(X1,X2,X4,X5)
    | hAPP(X1,X1,combi(X1),esk105_5(X1,X2,X3,X4,X5)) != hAPP(X1,X1,combi(X1),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),top_top(fun(X1,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1869,c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3276,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),esk111_5(X3,X1,X4,X5,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(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_1870,c_0_1517]),
    [final] ).

cnf(i_0_3277,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X5))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk69_5(X1,X2,X3,X4,X5))) != hAPP(X2,X2,combi(X2),esk69_5(X1,X2,X3,X4,X5)) ),
    inference(rw,[status(thm)],[i_0_1871,c_0_1517]),
    [final] ).

cnf(i_0_3278,plain,
    ( 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),X4),X3)),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(X1,bool),combi(fun(X1,bool)),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(rw,[status(thm)],[i_0_1872,c_0_1517]),
    [final] ).

cnf(i_0_3279,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5)
    | 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),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1873,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3280,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_3281,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),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_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_3282,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_3283,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),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_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_3284,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_3285,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),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_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_3286,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),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),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X4),X5)))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_3287,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_inf_inf(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)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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_1874]),
    [final] ).

cnf(i_0_3288,plain,
    ( hAPP(fun(X5,X2),fun(X5,X2),hAPP(fun(X2,X2),fun(fun(X5,X2),fun(X5,X2)),comp(X2,X2,X5),hAPP(X1,fun(X2,X2),X3,X6)),hAPP(fun(X5,X2),fun(X5,X2),hAPP(fun(X2,X2),fun(fun(X5,X2),fun(X5,X2)),comp(X2,X2,X5),hAPP(X1,fun(X2,X2),X3,X6)),X7)) = hAPP(fun(X5,X2),fun(X5,X2),hAPP(fun(X2,X2),fun(fun(X5,X2),fun(X5,X2)),comp(X2,X2,X5),hAPP(X1,fun(X2,X2),X3,X6)),X7)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1875]),
    [final] ).

cnf(i_0_3289,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk104_4(X3,X1,X2,X4))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool))))
    | ~ 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))))) ),
    inference(rw,[status(thm)],[i_0_1876,c_0_1517]),
    [final] ).

cnf(i_0_3290,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))
    | ~ 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_1821]),
    [final] ).

cnf(i_0_3291,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X5))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1877]),
    [final] ).

cnf(i_0_3292,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1858]),
    [final] ).

cnf(i_0_3293,plain,
    ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),semilattice_sup_sup(fun(nat,bool)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)),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),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1878]),
    [final] ).

cnf(i_0_3294,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(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_1793]),
    [final] ).

cnf(i_0_3295,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_1879]),
    [final] ).

cnf(i_0_3296,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_1880]),
    [final] ).

cnf(i_0_3297,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_1881]),
    [final] ).

cnf(i_0_3298,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_1882,c_0_1517]),
    [final] ).

cnf(i_0_3299,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1883]),
    [final] ).

cnf(i_0_3300,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1884]),
    [final] ).

cnf(i_0_3301,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X2)),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1883]),
    [final] ).

cnf(i_0_3302,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),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X2)),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1884]),
    [final] ).

cnf(i_0_3303,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_1885]),
    [final] ).

cnf(i_0_3304,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_1886]),
    [final] ).

cnf(i_0_3305,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_1887]),
    [final] ).

cnf(i_0_3306,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_1888]),
    [final] ).

cnf(i_0_3307,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(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)),top_top(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),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_1889]),
    [final] ).

cnf(i_0_3308,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,X1),fun(fun(nat,bool),bool),inj_on(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1286]),
    [final] ).

cnf(i_0_3309,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk167_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,bool,X2,esk166_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3310,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1823]),
    [final] ).

cnf(i_0_3311,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1823]),
    [final] ).

cnf(i_0_3312,plain,
    ( 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,bool),fun(fun(X1,X2),bool),extensional(X1,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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1890]),
    [final] ).

cnf(i_0_3313,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_1891]),
    [final] ).

cnf(i_0_3314,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),X4))
    | ~ 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1892]),
    [final] ).

cnf(i_0_3315,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),X4))
    | ~ 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1893]),
    [final] ).

cnf(i_0_3316,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(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1894]),
    [final] ).

cnf(i_0_3317,plain,
    ( 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)
    | 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,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1895,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3318,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_1896]),
    [final] ).

cnf(i_0_3319,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_1896]),
    [final] ).

cnf(i_0_3320,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_1897]),
    [final] ).

cnf(i_0_3321,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_1898]),
    [final] ).

cnf(i_0_3322,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_1899]),
    [final] ).

cnf(i_0_3323,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_1900]),
    [final] ).

cnf(i_0_3324,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_1795]),
    [final] ).

cnf(i_0_3325,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_1901]),
    [final] ).

cnf(i_0_3326,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_1797]),
    [final] ).

cnf(i_0_3327,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_1799]),
    [final] ).

cnf(i_0_3328,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_1902]),
    [final] ).

cnf(i_0_3329,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_1801]),
    [final] ).

cnf(i_0_3330,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_1903]),
    [final] ).

cnf(i_0_3331,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk134_5(X2,X1,X3,X4,X5)),X5))
    | hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1904]),
    [final] ).

cnf(i_0_3332,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk172_3(X1,X2,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2)))
    | hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(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,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1905]),
    [final] ).

cnf(i_0_3333,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X5),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,X2),fun(fun(X2,bool),fun(X2,bool)),image(X2,X2),X4),X3)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X2),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X2),fun(X2,X1)),comp(X2,X1,X2),X5),X4)),X3)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X2),fun(fun(X2,bool),bool),inj_on(X2,X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1906]),
    [final] ).

cnf(i_0_3334,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X4),X5)) = hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),hAPP(fun(X3,X1),fun(X3,X1),hAPP(fun(X1,X1),fun(fun(X3,X1),fun(X3,X1)),combb(X1,X1,X3),hAPP(X1,fun(X1,X1),times_times(X1),X2)),X4)),X5)
    | ~ semiring_0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1907]),
    [final] ).

cnf(i_0_3335,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk136_4(X1,X2,X3,X4)),X4))
    | hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4) = one_one(X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3336,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk105_5(X3,X1,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),top_top(fun(X3,bool)))))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X3,X1,X4,X5)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X4),top_top(fun(X3,bool)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1909,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3337,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,esk79_5(X2,X1,X3,X5,X4)) != hAPP(X1,X2,X5,esk79_5(X2,X1,X3,X5,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1829]),
    [final] ).

cnf(i_0_3338,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,esk79_5(X2,X1,X5,X3,X4)) != hAPP(X1,X2,X3,esk79_5(X2,X1,X5,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1829]),
    [final] ).

cnf(i_0_3339,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk69_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1236]),
    [final] ).

cnf(i_0_3340,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X3),X4))
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1910]),
    [final] ).

cnf(i_0_3341,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X3)),hAPP(nat,nat,suc,X4))) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),hAPP(fun(nat,nat),fun(nat,X1),hAPP(fun(nat,X1),fun(fun(nat,nat),fun(nat,X1)),combb(nat,X1,nat),X2),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X3),X4))
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1911]),
    [final] ).

cnf(i_0_3342,plain,
    ( 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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(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(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_1912]),
    [final] ).

cnf(i_0_3343,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1775]),
    [final] ).

cnf(i_0_3344,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1913]),
    [final] ).

cnf(i_0_3345,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1777]),
    [final] ).

cnf(i_0_3346,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(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_1914]),
    [final] ).

cnf(i_0_3347,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_1915]),
    [final] ).

cnf(i_0_3348,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_1810]),
    [final] ).

cnf(i_0_3349,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_1916]),
    [final] ).

cnf(i_0_3350,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_1811]),
    [final] ).

cnf(i_0_3351,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),esk107_4(X2,X1,X3,X4)),X4))
    | ~ 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),X3)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1717]),
    [final] ).

cnf(i_0_3352,plain,
    hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))),
    inference(split_conjunct,[status(thm)],[i_0_1917]),
    [final] ).

cnf(i_0_3353,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_1918]),
    [final] ).

cnf(i_0_3354,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1919]),
    [final] ).

cnf(i_0_3355,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(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)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),
    inference(split_conjunct,[status(thm)],[i_0_1920]),
    [final] ).

cnf(i_0_3356,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
    | ~ ordere453448008miring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1921]),
    [final] ).

cnf(i_0_3357,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere453448008miring(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),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1922]),
    [final] ).

cnf(i_0_3358,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),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),X3),zero_zero(X1)))
    | ~ ordere453448008miring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1921]),
    [final] ).

cnf(i_0_3359,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere453448008miring(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1923]),
    [final] ).

cnf(i_0_3360,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(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),zero_zero(X1)),X3))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3361,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),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),X3),zero_zero(X1)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3362,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
    | ~ ordere453448008miring(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1924]),
    [final] ).

cnf(i_0_3363,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ linord20386208strict(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),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1925]),
    [final] ).

cnf(i_0_3364,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
    | ~ linord20386208strict(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_3365,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)),zero_zero(X1)))
    | ~ linord20386208strict(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),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1927]),
    [final] ).

cnf(i_0_3366,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_1928]),
    [final] ).

cnf(i_0_3367,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_1929]),
    [final] ).

cnf(i_0_3368,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_1930]),
    [final] ).

cnf(i_0_3369,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_1931]),
    [final] ).

cnf(i_0_3370,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),X3))
    | ~ semilattice_sup(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),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1932]),
    [final] ).

cnf(i_0_3371,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),X3))
    | ~ semilattice_sup(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),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1933]),
    [final] ).

cnf(i_0_3372,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),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),X4),X3))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1884]),
    [final] ).

cnf(i_0_3373,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),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,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1934]),
    [final] ).

cnf(i_0_3374,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk109_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_1935,c_0_1517]),
    [final] ).

cnf(i_0_3375,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk103_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_1936,c_0_1517]),
    [final] ).

cnf(i_0_3376,plain,
    ( hAPP(fun(X3,bool),X1,hAPP(fun(X3,X1),fun(fun(X3,bool),X1),big_co1399186613setsum(X3,X1),X6),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X4),X5)) = hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),comp(X3,X1,X2),X6),X4)),X5)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X3),fun(fun(X2,bool),bool),inj_on(X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1937]),
    [final] ).

cnf(i_0_3377,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),X2) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_3378,plain,
    ( ~ linordered_ring(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1938]),
    [final] ).

cnf(i_0_3379,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),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_gr676655987ssThan(X1),X2),X4)
    | ~ 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),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1939]),
    [final] ).

cnf(i_0_3380,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
    | ~ 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),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1940]),
    [final] ).

cnf(i_0_3381,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X4)
    | ~ 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),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1941]),
    [final] ).

cnf(i_0_3382,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X4)
    | ~ 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_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1942]),
    [final] ).

cnf(i_0_3383,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
    | ~ 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_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1943]),
    [final] ).

cnf(i_0_3384,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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_atLeastAtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
    | ~ 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_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3385,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X4)
    | ~ 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),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1945]),
    [final] ).

cnf(i_0_3386,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X3),X4)) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X4)
    | ~ 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_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1946]),
    [final] ).

cnf(i_0_3387,plain,
    ( hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X4,X5)),hAPP(fun(X1,bool),fun(X2,X2),X4,X6)) = hAPP(fun(X1,bool),fun(X2,X2),X4,X5)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1947]),
    [final] ).

cnf(i_0_3388,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk15_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_3389,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1858]),
    [final] ).

cnf(i_0_3390,plain,
    ( hAPP(fun(X1,bool),fun(X2,X2),X4,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X5),X6)) = hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X4,X5)),hAPP(fun(X1,bool),fun(X2,X2),X4,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_3391,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(nat,X1,X4,X2)),hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X2),X3)))
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1949]),
    [final] ).

cnf(i_0_3392,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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_3393,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_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1775]),
    [final] ).

cnf(i_0_3394,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_1950,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3395,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_1951]),
    [final] ).

cnf(i_0_3396,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk117_4(X2,X1,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ 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),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1541]),
    [final] ).

cnf(i_0_3397,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_1952]),
    [final] ).

cnf(i_0_3398,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_1953]),
    [final] ).

cnf(i_0_3399,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_3400,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),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(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1955]),
    [final] ).

cnf(i_0_3401,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_1956,c_0_1517]),
    [final] ).

cnf(i_0_3402,plain,
    ( hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(fun(X1,bool),fun(X2,X2),X4,X5)),hAPP(X1,fun(X2,X2),X3,X6)) = hAPP(fun(X1,bool),fun(X2,X2),X4,X5)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1957]),
    [final] ).

cnf(i_0_3403,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3404,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk168_4(X1,X2,X3,X4)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3405,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),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_1894]),
    [final] ).

cnf(i_0_3406,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1958,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3407,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1959,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3408,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1960,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3409,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X2))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1961,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3410,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_3411,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1962]),
    [final] ).

cnf(i_0_3412,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1963]),
    [final] ).

cnf(i_0_3413,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_3414,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1963]),
    [final] ).

cnf(i_0_3415,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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_1964]),
    [final] ).

cnf(i_0_3416,plain,
    ( 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)),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),fun(X1,bool),combi(fun(X1,bool)),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_1965,c_0_1517]),
    [final] ).

cnf(i_0_3417,plain,
    ( 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)),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),fun(X1,bool),combi(fun(X1,bool)),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_1966,c_0_1517]),
    [final] ).

cnf(i_0_3418,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_1967]),
    [final] ).

cnf(i_0_3419,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_1968]),
    [final] ).

cnf(i_0_3420,plain,
    ( hBOOL(hAPP(X1,bool,X4,X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X4,X3,X5)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3421,plain,
    ( hBOOL(hAPP(X1,bool,X4,X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk169_4(X1,X4,X5,X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),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_1819]),
    [final] ).

cnf(i_0_3422,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1969]),
    [final] ).

cnf(i_0_3423,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1970]),
    [final] ).

cnf(i_0_3424,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ linord20386208strict(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1971]),
    [final] ).

cnf(i_0_3425,plain,
    ( hAPP(X1,X4,hAPP(fun(X1,X5),fun(X1,X4),hAPP(fun(X5,X4),fun(fun(X1,X5),fun(X1,X4)),hAPP(fun(X1,bool),fun(fun(X5,X4),fun(fun(X1,X5),fun(X1,X4))),compose(X1,X5,X4),X3),X6),X7),X2) = hAPP(X5,X4,X6,hAPP(X1,X5,X7,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_1972]),
    [final] ).

cnf(i_0_3426,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_1973]),
    [final] ).

cnf(i_0_3427,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_1974]),
    [final] ).

cnf(i_0_3428,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ 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),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_1975]),
    [final] ).

cnf(i_0_3429,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_1976]),
    [final] ).

cnf(i_0_3430,plain,
    ( 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)),the_inv_into(X1,X2),X4),X3)),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),fun(X1,bool),combi(fun(X1,bool)),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_1977,c_0_1517]),
    [final] ).

cnf(i_0_3431,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1978]),
    [final] ).

cnf(i_0_3432,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1979]),
    [final] ).

cnf(i_0_3433,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(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X5)) = hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),semilattice_sup_sup(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)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_1980]),
    [final] ).

cnf(i_0_3434,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_1981]),
    [final] ).

cnf(i_0_3435,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_1982]),
    [final] ).

cnf(i_0_3436,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
    inference(rw,[status(thm)],[i_0_1983,c_0_1517]),
    [final] ).

cnf(i_0_3437,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) != hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),X3),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)),X4))) ),
    inference(rw,[status(thm)],[i_0_1984,c_0_1517]),
    [final] ).

cnf(i_0_3438,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X5))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1985]),
    [final] ).

cnf(i_0_3439,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_1986]),
    [final] ).

cnf(i_0_3440,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1987]),
    [final] ).

cnf(i_0_3441,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X3,X1,X4,esk116_4(X1,X3,X2,X4))
    | ~ 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))))) ),
    inference(rw,[status(thm)],[i_0_1988,c_0_1517]),
    [final] ).

cnf(i_0_3442,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_1989]),
    [final] ).

cnf(i_0_3443,plain,
    ( 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))
    | hAPP(X1,X2,X3,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),esk106_3(X1,X2,X3))) != hAPP(X2,X2,combi(X2),esk106_3(X1,X2,X3)) ),
    inference(rw,[status(thm)],[i_0_1990,c_0_1517]),
    [final] ).

cnf(i_0_3444,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(X2,fun(fun(X1,bool),X2),hAPP(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2)),hAPP(fun(X2,fun(X2,X2)),fun(fun(X1,X2),fun(X2,fun(fun(X1,bool),X2))),finite_fold_image(X2,X1),times_times(X2)),X3),one_one(X2)),X4) = one_one(X2)
    | hAPP(X1,X2,X3,esk136_4(X1,X2,X3,X4)) != one_one(X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ comm_monoid_mult(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3445,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1991]),
    [final] ).

cnf(i_0_3446,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk163_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3447,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk115_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1993]),
    [final] ).

cnf(i_0_3448,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),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),times_times(X1),X2),X3)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3449,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),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),times_times(X1),X3),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3450,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),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3451,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),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3452,plain,
    ( hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),X4),X2) = hAPP(fun(X1,bool),X3,hAPP(X3,fun(fun(X1,bool),X3),hAPP(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3)),hAPP(fun(X3,fun(X3,X3)),fun(fun(X1,X3),fun(X3,fun(fun(X1,bool),X3))),finite_fold_image(X3,X1),plus_plus(X3)),X4),zero_zero(X3)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1995]),
    [final] ).

cnf(i_0_3453,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),plus_plus(X1)),X4),zero_zero(X1)),X3)
    | ~ comm_monoid_add(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1996]),
    [final] ).

cnf(i_0_3454,plain,
    ( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X5) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X4),X5)
    | hAPP(X1,X2,X3,esk134_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk134_5(X2,X1,X3,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1904]),
    [final] ).

cnf(i_0_3455,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_1879]),
    [final] ).

cnf(i_0_3456,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_1880]),
    [final] ).

cnf(i_0_3457,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_1881]),
    [final] ).

cnf(i_0_3458,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk164_2(X1,X2)),X2))
    | hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1997]),
    [final] ).

cnf(i_0_3459,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk112_2(X1,X2)),X2))
    | hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1998]),
    [final] ).

cnf(i_0_3460,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),X3))
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1999]),
    [final] ).

cnf(i_0_3461,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X4),X2)),X3))
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2000]),
    [final] ).

cnf(i_0_3462,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),X3))
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2001]),
    [final] ).

cnf(i_0_3463,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X4),X2)),X3))
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2002]),
    [final] ).

cnf(i_0_3464,plain,
    hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),hAPP(fun(X1,X5),fun(X1,X2),hAPP(fun(X5,X2),fun(fun(X1,X5),fun(X1,X2)),comp(X5,X2,X1),X6),X7)) = hAPP(fun(X1,X5),fun(X1,X3),hAPP(fun(X5,X3),fun(fun(X1,X5),fun(X1,X3)),comp(X5,X3,X1),hAPP(fun(X5,X2),fun(X5,X3),hAPP(fun(X2,X3),fun(fun(X5,X2),fun(X5,X3)),comp(X2,X3,X5),X4),X6)),X7),
    inference(split_conjunct,[status(thm)],[i_0_2003]),
    [final] ).

cnf(i_0_3465,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_2004]),
    [final] ).

cnf(i_0_3466,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_2005]),
    [final] ).

cnf(i_0_3467,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_2005]),
    [final] ).

cnf(i_0_3468,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_2006]),
    [final] ).

cnf(i_0_3469,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_2007]),
    [final] ).

cnf(i_0_3470,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),esk27_2(X1,X2))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2008,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3471,plain,
    hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),hAPP(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))),compose(X1,X2,X3),X4),X5),X6) = hAPP(fun(X1,bool),fun(X1,X3),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X1,X3)),restrict(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X5),X6)),X4),
    inference(split_conjunct,[status(thm)],[i_0_2009]),
    [final] ).

cnf(i_0_3472,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,esk57_4(X1,X2,X3,X4)),esk58_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_2010]),
    [final] ).

cnf(i_0_3473,plain,
    ( hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),hAPP(fun(X1,X2),fun(X1,X4),hAPP(fun(X2,X4),fun(fun(X1,X2),fun(X1,X4)),comp(X2,X4,X1),X5),X3)),top_top(fun(X1,bool))) = top_top(fun(X4,bool))
    | 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))
    | hAPP(fun(X2,bool),fun(X4,bool),hAPP(fun(X2,X4),fun(fun(X2,bool),fun(X4,bool)),image(X2,X4),X5),top_top(fun(X2,bool))) != top_top(fun(X4,bool)) ),
    inference(split_conjunct,[status(thm)],[i_0_2011]),
    [final] ).

cnf(i_0_3474,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_2012,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3475,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_2013,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3476,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_2014,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3477,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_2015,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3478,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_2016,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3479,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),ord_greaterThan(X1),X2)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2017]),
    [final] ).

cnf(i_0_3480,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(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(X1,fun(X1,bool),ord_atLeast(X1),X2)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2018]),
    [final] ).

cnf(i_0_3481,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk18_2(X1,X2)),arrow_301600364e_Prof))
    | hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1834]),
    [final] ).

cnf(i_0_3482,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_2019,c_0_1517]),
    [final] ).

cnf(i_0_3483,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_2020,c_0_1517]),
    [final] ).

cnf(i_0_3484,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_2021,c_0_1517]),
    [final] ).

cnf(i_0_3485,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),times_times(X1),X2),X3)))
    | ~ 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))
    | ~ ordered_ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2022]),
    [final] ).

cnf(i_0_3486,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),times_times(X1),X2),X3)))
    | ~ ordere453448008miring(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_2023]),
    [final] ).

cnf(i_0_3487,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),times_times(X1),X2),X3)))
    | ~ 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))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3488,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_2024]),
    [final] ).

cnf(i_0_3489,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ linord20386208strict(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_2025]),
    [final] ).

cnf(i_0_3490,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_2026]),
    [final] ).

cnf(i_0_3491,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_2027]),
    [final] ).

cnf(i_0_3492,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_2028]),
    [final] ).

cnf(i_0_3493,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2029]),
    [final] ).

cnf(i_0_3494,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_2030]),
    [final] ).

cnf(i_0_3495,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),times_times(X1),X2),X3)))
    | ~ 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)))
    | ~ ordered_ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2022]),
    [final] ).

cnf(i_0_3496,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),times_times(X1),X2),X3)))
    | ~ ordered_ring(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_2031]),
    [final] ).

cnf(i_0_3497,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),times_times(X1),X2),X3)))
    | ~ 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)))
    | ~ linord581940658strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1994]),
    [final] ).

cnf(i_0_3498,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
    | ~ linord581940658strict(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_2032]),
    [final] ).

cnf(i_0_3499,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_2033]),
    [final] ).

cnf(i_0_3500,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_2034]),
    [final] ).

cnf(i_0_3501,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_2035]),
    [final] ).

cnf(i_0_3502,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_2036]),
    [final] ).

cnf(i_0_3503,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_2037]),
    [final] ).

cnf(i_0_3504,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
    | ~ 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))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2038]),
    [final] ).

cnf(i_0_3505,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
    | ~ semilattice_inf(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),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2039]),
    [final] ).

cnf(i_0_3506,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)))
    | ~ semilattice_inf(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),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2040]),
    [final] ).

cnf(i_0_3507,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),esk100_3(X1,X2,X3))))
    | ~ linordered_field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2041]),
    [final] ).

cnf(i_0_3508,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),esk20_0)),
    inference(split_conjunct,[status(thm)],[i_0_2042]),
    [final] ).

cnf(i_0_3509,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),b),a)),lba)),
    inference(split_conjunct,[status(thm)],[fact_39__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096]),
    [final] ).

cnf(i_0_3510,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),esk19_0)),
    inference(split_conjunct,[status(thm)],[i_0_2043]),
    [final] ).

cnf(i_0_3511,plain,
    hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),a),b)),lab)),
    inference(split_conjunct,[status(thm)],[fact_38__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096]),
    [final] ).

cnf(i_0_3512,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_2044]),
    [final] ).

cnf(i_0_3513,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)),comp(X3,X2,X1),X4),X5)),X6) = 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),X6)),
    inference(split_conjunct,[status(thm)],[i_0_2045]),
    [final] ).

cnf(i_0_3514,plain,
    ( hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,esk164_2(X1,X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1997]),
    [final] ).

cnf(i_0_3515,plain,
    ( hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,esk112_2(X1,X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1998]),
    [final] ).

cnf(i_0_3516,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_2046]),
    [final] ).

cnf(i_0_3517,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk163_2(X1,X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3518,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk115_2(X1,X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1993]),
    [final] ).

cnf(i_0_3519,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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_2047]),
    [final] ).

cnf(i_0_3520,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
    | ~ distrib_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2048]),
    [final] ).

cnf(i_0_3521,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
    | ~ distrib_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2049]),
    [final] ).

cnf(i_0_3522,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ comm_semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2050]),
    [final] ).

cnf(i_0_3523,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2051]),
    [final] ).

cnf(i_0_3524,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)))
    | ~ 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)) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3525,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_2053,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3526,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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_2054,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3527,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk176_4(X1,X2,X3,X4)),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | hAPP(X1,nat,X2,X4) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]),
    [final] ).

cnf(i_0_3528,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_2055]),
    [final] ).

cnf(i_0_3529,plain,
    ( 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)),top_top(fun(X2,bool))) = 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_2056]),
    [final] ).

cnf(i_0_3530,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2057]),
    [final] ).

cnf(i_0_3531,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1892]),
    [final] ).

cnf(i_0_3532,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2058]),
    [final] ).

cnf(i_0_3533,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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_2059]),
    [final] ).

cnf(i_0_3534,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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_1892]),
    [final] ).

cnf(i_0_3535,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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),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_2058]),
    [final] ).

cnf(i_0_3536,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_2060]),
    [final] ).

cnf(i_0_3537,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)),X4) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)),
    inference(split_conjunct,[status(thm)],[i_0_2061]),
    [final] ).

cnf(i_0_3538,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2062]),
    [final] ).

cnf(i_0_3539,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_2063,c_0_1517]),
    [final] ).

cnf(i_0_3540,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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_2064,c_0_1517]),
    [final] ).

cnf(i_0_3541,plain,
    ( ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(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) ),
    inference(split_conjunct,[status(thm)],[i_0_2065]),
    [final] ).

cnf(i_0_3542,plain,
    ( hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X2),hAPP(nat,nat,suc,X1))) = zero_zero(X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1786]),
    [final] ).

cnf(i_0_3543,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_2066]),
    [final] ).

cnf(i_0_3544,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_2067]),
    [final] ).

cnf(i_0_3545,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),semilattice_inf_inf(X1),X3),X4)))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2038]),
    [final] ).

cnf(i_0_3546,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),semilattice_inf_inf(X1),X3),X4)))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2068]),
    [final] ).

cnf(i_0_3547,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),semilattice_inf_inf(X1),X4),X3)))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2038]),
    [final] ).

cnf(i_0_3548,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),semilattice_inf_inf(X1),X4),X3)))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2068]),
    [final] ).

cnf(i_0_3549,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X5) = hAPP(X1,X1,combi(X1),X6)
    | hAPP(X1,X1,combi(X1),X3) != hAPP(X1,X1,combi(X1),X4)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X5)) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X6))
    | ~ semiri456707255roduct(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2069,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3550,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_1851]),
    [final] ).

cnf(i_0_3551,plain,
    ( hBOOL(hAPP(X1,bool,X2,X4))
    | hBOOL(hAPP(X1,bool,X3,X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2070]),
    [final] ).

cnf(i_0_3552,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[i_0_2071,c_0_1517]),
    [final] ).

cnf(i_0_3553,plain,
    ( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[i_0_2072,c_0_1517]),
    [final] ).

cnf(i_0_3554,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_2073]),
    [final] ).

cnf(i_0_3555,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_2074]),
    [final] ).

cnf(i_0_3556,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_2075]),
    [final] ).

cnf(i_0_3557,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_2076]),
    [final] ).

cnf(i_0_3558,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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3559,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)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3560,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk178_4(X1,X2,X3,X4)),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | hAPP(X1,nat,X2,X4) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]),
    [final] ).

cnf(i_0_3561,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_2077,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3562,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3563,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3564,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_2079]),
    [final] ).

cnf(i_0_3565,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_2080]),
    [final] ).

cnf(i_0_3566,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_2081]),
    [final] ).

cnf(i_0_3567,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_2082]),
    [final] ).

cnf(i_0_3568,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_2083]),
    [final] ).

cnf(i_0_3569,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_2084]),
    [final] ).

cnf(i_0_3570,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk162_2(X1,X2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3571,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk114_2(X1,X2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1993]),
    [final] ).

cnf(i_0_3572,plain,
    hAPP(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool))),combi(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(fun(X2,X1),fun(fun(X2,bool),X1)),bool)))),finite_folding_image(X1,X2)) = finite_folding_image(X1,X2),
    inference(rw,[status(thm)],[i_0_2085,c_0_1517]),
    [final] ).

cnf(i_0_3573,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2086]),
    [final] ).

cnf(i_0_3574,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X4),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2086]),
    [final] ).

cnf(i_0_3575,plain,
    ( hBOOL(hAPP(X1,bool,X2,X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2087]),
    [final] ).

cnf(i_0_3576,plain,
    ( hBOOL(hAPP(X1,bool,X3,X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2088]),
    [final] ).

cnf(i_0_3577,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_2089]),
    [final] ).

cnf(i_0_3578,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_2090]),
    [final] ).

cnf(i_0_3579,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_2091]),
    [final] ).

cnf(i_0_3580,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_2092]),
    [final] ).

cnf(i_0_3581,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_2093]),
    [final] ).

cnf(i_0_3582,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_2094,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3583,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_2095,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3584,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_2096,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3585,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_2097,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3586,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_2098,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3587,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_2099]),
    [final] ).

cnf(i_0_3588,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk165_2(X1,X2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2)))
    | hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1997]),
    [final] ).

cnf(i_0_3589,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk113_2(X1,X2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X2)))
    | hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1998]),
    [final] ).

cnf(i_0_3590,plain,
    ( hAPP(fun(X2,X2),fun(X2,X2),hAPP(fun(X2,X2),fun(fun(X2,X2),fun(X2,X2)),comp(X2,X2,X2),hAPP(X1,fun(X2,X2),X3,X5)),hAPP(X1,fun(X2,X2),X3,X5)) = hAPP(X1,fun(X2,X2),X3,X5)
    | ~ hBOOL(hAPP(fun(fun(X1,bool),fun(X2,X2)),bool,hAPP(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool),finite_folding_idem(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2100]),
    [final] ).

cnf(i_0_3591,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr676655987ssThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2101]),
    [final] ).

cnf(i_0_3592,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_gr1471790799AtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3593,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2103]),
    [final] ).

cnf(i_0_3594,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastAtMost(X1),X2),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2104]),
    [final] ).

cnf(i_0_3595,plain,
    ( hAPP(X4,X2,hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),comp(X1,X2,X4),X3),X5),X6) = hAPP(X9,X2,hAPP(fun(X9,X7),fun(X9,X2),hAPP(fun(X7,X2),fun(fun(X9,X7),fun(X9,X2)),comp(X7,X2,X9),X8),X10),X11)
    | hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) != hAPP(X7,X2,X8,hAPP(X9,X7,X10,X11)) ),
    inference(split_conjunct,[status(thm)],[i_0_2105]),
    [final] ).

cnf(i_0_3596,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))),X3)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2106]),
    [final] ).

cnf(i_0_3597,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
    | ~ distrib_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2107]),
    [final] ).

cnf(i_0_3598,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
    | ~ distrib_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2108]),
    [final] ).

cnf(i_0_3599,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(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),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2109]),
    [final] ).

cnf(i_0_3600,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),X3)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2110]),
    [final] ).

cnf(i_0_3601,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_2111]),
    [final] ).

cnf(i_0_3602,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2112]),
    [final] ).

cnf(i_0_3603,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X2))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2113]),
    [final] ).

cnf(i_0_3604,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2114]),
    [final] ).

cnf(i_0_3605,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X3))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2115]),
    [final] ).

cnf(i_0_3606,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_2005]),
    [final] ).

cnf(i_0_3607,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_2116]),
    [final] ).

cnf(i_0_3608,plain,
    ( hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,X2),fun(X1,X2),combi(fun(X1,X2)),X3)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
    inference(rw,[status(thm)],[i_0_2117,c_0_1517]),
    [final] ).

cnf(i_0_3609,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_2118]),
    [final] ).

cnf(i_0_3610,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_2119]),
    [final] ).

cnf(i_0_3611,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_2120]),
    [final] ).

cnf(i_0_3612,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_2121]),
    [final] ).

cnf(i_0_3613,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_2122]),
    [final] ).

cnf(i_0_3614,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk15_1(X1)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_3615,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk11_1(X1)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3616,plain,
    ( hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),esk10_1(X1)),arrow_301600364e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_3617,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_2123]),
    [final] ).

cnf(i_0_3618,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_2124]),
    [final] ).

cnf(i_0_3619,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_1816]),
    [final] ).

cnf(i_0_3620,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_2125]),
    [final] ).

cnf(i_0_3621,plain,
    ( 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),ord_greaterThan(X1),X3)),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2017]),
    [final] ).

cnf(i_0_3622,plain,
    ( 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),ord_atLeast(X1),X3)),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2018]),
    [final] ).

cnf(i_0_3623,plain,
    ( hAPP(X1,X2,X3,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),X4)) = hAPP(X2,X2,combi(X2),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_2126,c_0_1517]),
    [final] ).

cnf(i_0_3624,plain,
    ( hAPP(X1,X2,X3,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),X4)) = hAPP(X2,X2,combi(X2),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_2127,c_0_1517]),
    [final] ).

cnf(i_0_3625,plain,
    ( hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),X3)) = hAPP(fun(nat,bool),X1,hAPP(fun(nat,X1),fun(fun(nat,bool),X1),big_co1399186613setsum(nat,X1),X2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),X3))
    | ~ comm_monoid_add(X1)
    | hAPP(nat,X1,X2,zero_zero(nat)) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2128]),
    [final] ).

cnf(i_0_3626,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk121_2(X1,X2)),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)),esk120_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_2129,c_0_1517]),
    [final] ).

cnf(i_0_3627,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(nat,bool),fun(X1,bool),hAPP(fun(nat,X1),fun(fun(nat,bool),fun(X1,bool)),image(nat,X1),esk119_2(X1,X2)),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)),esk118_2(X1,X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(rw,[status(thm)],[i_0_2130,c_0_1517]),
    [final] ).

cnf(i_0_3628,plain,
    ( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,zero_zero(nat))),X2)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),X2))
    | hAPP(nat,nat,X1,zero_zero(nat)) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2131]),
    [final] ).

cnf(i_0_3629,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_2132,c_0_1517]),
    [final] ).

cnf(i_0_3630,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_3631,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_2134]),
    [final] ).

cnf(i_0_3632,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,esk57_4(X1,X2,X4,X3)),esk58_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_2010]),
    [final] ).

cnf(i_0_3633,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_2046]),
    [final] ).

cnf(i_0_3634,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X5)
    | 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),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(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_2135,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3635,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(X2,X1,X4,hAPP(X1,X2,X3,esk110_4(X1,X2,X4,X3))) != hAPP(X1,X1,combi(X1),esk110_4(X1,X2,X4,X3))
    | 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)],[inference(rw,[status(thm)],[i_0_2136,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3636,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_2066]),
    [final] ).

cnf(i_0_3637,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_2067]),
    [final] ).

cnf(i_0_3638,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2137]),
    [final] ).

cnf(i_0_3639,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X3)))
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2138]),
    [final] ).

cnf(i_0_3640,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)))
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2139]),
    [final] ).

cnf(i_0_3641,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X4),X3)))
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2140]),
    [final] ).

cnf(i_0_3642,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X4) = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(X1,nat,X3,X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),esk176_4(X1,X3,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2141,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3643,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_2142,c_0_1517]),
    [final] ).

cnf(i_0_3644,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_2143]),
    [final] ).

cnf(i_0_3645,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_2144]),
    [final] ).

cnf(i_0_3646,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_2145,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3647,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_2146,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3648,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_2147]),
    [final] ).

cnf(i_0_3649,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_2148]),
    [final] ).

cnf(i_0_3650,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_2004]),
    [final] ).

cnf(i_0_3651,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_2004]),
    [final] ).

cnf(i_0_3652,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_2149]),
    [final] ).

cnf(i_0_3653,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_2150]),
    [final] ).

cnf(i_0_3654,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_2151]),
    [final] ).

cnf(i_0_3655,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_2152]),
    [final] ).

cnf(i_0_3656,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_2153]),
    [final] ).

cnf(i_0_3657,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_2154]),
    [final] ).

cnf(i_0_3658,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_2155]),
    [final] ).

cnf(i_0_3659,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_2156]),
    [final] ).

cnf(i_0_3660,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_2157,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3661,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk95_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_2158]),
    [final] ).

cnf(i_0_3662,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_2159]),
    [final] ).

cnf(i_0_3663,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_2160]),
    [final] ).

cnf(i_0_3664,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_2161]),
    [final] ).

cnf(i_0_3665,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_2162]),
    [final] ).

cnf(i_0_3666,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_2163]),
    [final] ).

cnf(i_0_3667,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_2164]),
    [final] ).

cnf(i_0_3668,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4)),
    inference(split_conjunct,[status(thm)],[i_0_2165]),
    [final] ).

cnf(i_0_3669,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3670,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2166]),
    [final] ).

cnf(i_0_3671,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_2089]),
    [final] ).

cnf(i_0_3672,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_2090]),
    [final] ).

cnf(i_0_3673,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_2167]),
    [final] ).

cnf(i_0_3674,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(X1,nat,X2,esk176_4(X1,X2,X3,X4)) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | hAPP(X1,nat,X2,X4) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]),
    [final] ).

cnf(i_0_3675,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X1,nat,X4,esk146_3(X1,X4,X2))),hAPP(X1,nat,X4,X3)))
    | ~ hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_3676,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_2148]),
    [final] ).

cnf(i_0_3677,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_2134]),
    [final] ).

cnf(i_0_3678,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_2169,c_0_1517]),
    [final] ).

cnf(i_0_3679,plain,
    ( hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),the_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_2170,c_0_1517]),
    [final] ).

cnf(i_0_3680,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,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4)),X4) = hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_2171]),
    [final] ).

cnf(i_0_3681,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),collect(X1),X3)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(X1,bool,X2,esk150_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_3682,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))
    | one_one(nat) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1905]),
    [final] ).

cnf(i_0_3683,plain,
    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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_2173]),
    [final] ).

cnf(i_0_3684,plain,
    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,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2174]),
    [final] ).

cnf(i_0_3685,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2175]),
    [final] ).

cnf(i_0_3686,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_2176,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3687,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_2046]),
    [final] ).

cnf(i_0_3688,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X3),X4) = one_one(nat)
    | hAPP(X1,nat,X3,X2) != one_one(nat)
    | hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),esk178_4(X1,X3,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2177,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3689,plain,
    ( 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)
    | 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,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_2178,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3690,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_2179,c_0_1517]),
    [final] ).

cnf(i_0_3691,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_2180,c_0_1517]),
    [final] ).

cnf(i_0_3692,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_2181]),
    [final] ).

cnf(i_0_3693,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_2182]),
    [final] ).

cnf(i_0_3694,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_2183]),
    [final] ).

cnf(i_0_3695,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_2184]),
    [final] ).

cnf(i_0_3696,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_2185]),
    [final] ).

cnf(i_0_3697,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_2186]),
    [final] ).

cnf(i_0_3698,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_2187]),
    [final] ).

cnf(i_0_3699,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_2188]),
    [final] ).

cnf(i_0_3700,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool,hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),bool),member(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p),arrow_301600364e_Prof)),
    inference(split_conjunct,[status(thm)],[fact_3__096P_A_058_AProf_096]),
    [final] ).

cnf(i_0_3701,plain,
    ( hAPP(X1,nat,X4,X2) = zero_zero(nat)
    | hAPP(X1,X1,combi(X1),esk175_3(X1,X4,X3)) = hAPP(X1,X1,combi(X1),X2)
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X4),X3) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2189,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3702,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_2190]),
    [final] ).

cnf(i_0_3703,plain,
    arrow_301600364e_Prof = hAPP(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),hAPP(fun(arrow_1998540521e_indi,bool),fun(fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),pi(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),top_top(fun(arrow_1998540521e_indi,bool))),hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(arrow_1998540521e_indi,fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),arrow_1998540521e_indi),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_141_Prof__def]),
    [final] ).

cnf(i_0_3704,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_2191]),
    [final] ).

cnf(i_0_3705,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),one_one(X1))),X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2192]),
    [final] ).

cnf(i_0_3706,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X3) != zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ linord581940658strict(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2193,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3707,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3708,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_3709,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2196]),
    [final] ).

cnf(i_0_3710,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2197]),
    [final] ).

cnf(i_0_3711,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2198]),
    [final] ).

cnf(i_0_3712,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2199]),
    [final] ).

cnf(i_0_3713,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2200]),
    [final] ).

cnf(i_0_3714,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4))
    | ~ ab_semigroup_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2201]),
    [final] ).

cnf(i_0_3715,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_2202]),
    [final] ).

cnf(i_0_3716,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_2203]),
    [final] ).

cnf(i_0_3717,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),X4)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2204]),
    [final] ).

cnf(i_0_3718,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_2205]),
    [final] ).

cnf(i_0_3719,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_2206]),
    [final] ).

cnf(i_0_3720,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_2207]),
    [final] ).

cnf(i_0_3721,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk150_3(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),collect(X1),X2)),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_3722,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = one_one(nat)
    | hAPP(X1,nat,X2,esk178_4(X1,X2,X3,X4)) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | hAPP(X1,nat,X2,X4) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]),
    [final] ).

cnf(i_0_3723,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_2208]),
    [final] ).

cnf(i_0_3724,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_2209]),
    [final] ).

cnf(i_0_3725,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2210]),
    [final] ).

cnf(i_0_3726,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2211]),
    [final] ).

cnf(i_0_3727,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_2212]),
    [final] ).

cnf(i_0_3728,plain,
    ( hAPP(fun(nat,bool),X3,hAPP(fun(nat,X3),fun(fun(nat,bool),X3),big_co1399186613setsum(nat,X3),X4),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,suc,X1))) = zero_zero(X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1825]),
    [final] ).

cnf(i_0_3729,plain,
    ( hAPP(X1,nat,X4,X2) = zero_zero(nat)
    | hAPP(X1,X1,combi(X1),esk177_3(X1,X4,X3)) = hAPP(X1,X1,combi(X1),X2)
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X4),X3) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2213,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3730,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2214]),
    [final] ).

cnf(i_0_3731,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2214]),
    [final] ).

cnf(i_0_3732,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_2215,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3733,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_2216,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3734,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)) ),
    inference(split_conjunct,[status(thm)],[i_0_2217]),
    [final] ).

cnf(i_0_3735,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_2218]),
    [final] ).

cnf(i_0_3736,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_2161]),
    [final] ).

cnf(i_0_3737,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_2162]),
    [final] ).

cnf(i_0_3738,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2219]),
    [final] ).

cnf(i_0_3739,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2220]),
    [final] ).

cnf(i_0_3740,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2221]),
    [final] ).

cnf(i_0_3741,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2220]),
    [final] ).

cnf(i_0_3742,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_2222]),
    [final] ).

cnf(i_0_3743,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_2223]),
    [final] ).

cnf(i_0_3744,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_2224,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3745,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk78_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_1349]),
    [final] ).

cnf(i_0_3746,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk77_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_1349]),
    [final] ).

cnf(i_0_3747,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk32_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_1263]),
    [final] ).

cnf(i_0_3748,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_1263]),
    [final] ).

cnf(i_0_3749,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_2225]),
    [final] ).

cnf(i_0_3750,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_2226]),
    [final] ).

cnf(i_0_3751,plain,
    ( X1 = hAPP(nat,nat,suc,esk95_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_2158]),
    [final] ).

cnf(i_0_3752,plain,
    ( X2 = hAPP(nat,nat,suc,esk93_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_2227]),
    [final] ).

cnf(i_0_3753,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk87_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_2228]),
    [final] ).

cnf(i_0_3754,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_2229]),
    [final] ).

cnf(i_0_3755,plain,
    ( hBOOL(hAPP(X1,bool,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X4,esk169_4(X1,X4,X3,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3756,plain,
    ( hBOOL(hAPP(X1,bool,X4,X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X4,esk169_4(X1,X4,X5,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_1819]),
    [final] ).

cnf(i_0_3757,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_2230]),
    [final] ).

cnf(i_0_3758,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_2231]),
    [final] ).

cnf(i_0_3759,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),esk60_3(X1,X2,X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2232]),
    [final] ).

cnf(i_0_3760,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_2055]),
    [final] ).

cnf(i_0_3761,plain,
    ( hAPP(X2,X3,X4,hAPP(X1,X2,X5,X9)) = hAPP(X6,X3,X7,hAPP(X1,X6,X8,X9))
    | hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),X5) != hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),comp(X6,X3,X1),X7),X8) ),
    inference(split_conjunct,[status(thm)],[i_0_2233]),
    [final] ).

cnf(i_0_3762,plain,
    ( hAPP(X2,X3,X4,hAPP(X1,X2,X5,X9)) = hAPP(X6,X3,X7,hAPP(X1,X6,X8,X9))
    | hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),X5) != hAPP(fun(X1,X6),fun(X1,X3),hAPP(fun(X6,X3),fun(fun(X1,X6),fun(X1,X3)),comp(X6,X3,X1),X7),X8) ),
    inference(split_conjunct,[status(thm)],[i_0_2234]),
    [final] ).

cnf(i_0_3763,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk87_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_2228]),
    [final] ).

cnf(i_0_3764,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_2134]),
    [final] ).

cnf(i_0_3765,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_2235]),
    [final] ).

cnf(i_0_3766,plain,
    ( hAPP(X1,nat,X2,X4) = zero_zero(nat)
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_3767,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_2237]),
    [final] ).

cnf(i_0_3768,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_2238]),
    [final] ).

cnf(i_0_3769,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_2239]),
    [final] ).

cnf(i_0_3770,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_2240]),
    [final] ).

cnf(i_0_3771,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_2241]),
    [final] ).

cnf(i_0_3772,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_2242,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3773,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_2243,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3774,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_2244,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3775,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_2245,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3776,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),hAPP(X2,fun(X3,X2),combk(X2,X3),X4)),X5),X6) = hAPP(X2,X2,combi(X2),X4),
    inference(rw,[status(thm)],[i_0_2246,c_0_1517]),
    [final] ).

cnf(i_0_3777,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_2247]),
    [final] ).

cnf(i_0_3778,plain,
    ( X2 = X3
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_3779,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2211]),
    [final] ).

cnf(i_0_3780,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2210]),
    [final] ).

cnf(i_0_3781,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_2249]),
    [final] ).

cnf(i_0_3782,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_1301]),
    [final] ).

cnf(i_0_3783,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_1302]),
    [final] ).

cnf(i_0_3784,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_2231]),
    [final] ).

cnf(i_0_3785,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),esk71_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_2250]),
    [final] ).

cnf(i_0_3786,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(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_2251]),
    [final] ).

cnf(i_0_3787,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2252]),
    [final] ).

cnf(i_0_3788,plain,
    hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2253]),
    [final] ).

cnf(i_0_3789,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X3))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3790,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk168_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(X1,bool,X2,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_3791,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk80_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_2254]),
    [final] ).

cnf(i_0_3792,plain,
    ( 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))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk128_4(X1,X2,X3,X4))) != hAPP(X2,X2,combi(X2),esk128_4(X1,X2,X3,X4)) ),
    inference(rw,[status(thm)],[i_0_2255,c_0_1517]),
    [final] ).

cnf(i_0_3793,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk175_3(X1,X2,X3)),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]),
    [final] ).

cnf(i_0_3794,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_2125]),
    [final] ).

cnf(i_0_3795,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_2256]),
    [final] ).

cnf(i_0_3796,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_2257]),
    [final] ).

cnf(i_0_3797,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_2229]),
    [final] ).

cnf(i_0_3798,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_2258]),
    [final] ).

cnf(i_0_3799,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_2259]),
    [final] ).

cnf(i_0_3800,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_2260]),
    [final] ).

cnf(i_0_3801,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_2261]),
    [final] ).

cnf(i_0_3802,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_2262]),
    [final] ).

cnf(i_0_3803,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_2263]),
    [final] ).

cnf(i_0_3804,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_2264]),
    [final] ).

cnf(i_0_3805,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_1353]),
    [final] ).

cnf(i_0_3806,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_2265]),
    [final] ).

cnf(i_0_3807,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_2206]),
    [final] ).

cnf(i_0_3808,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_2225]),
    [final] ).

cnf(i_0_3809,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_2266]),
    [final] ).

cnf(i_0_3810,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_2267]),
    [final] ).

cnf(i_0_3811,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_2241]),
    [final] ).

cnf(i_0_3812,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_2237]),
    [final] ).

cnf(i_0_3813,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_2268]),
    [final] ).

cnf(i_0_3814,plain,
    ( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_sup_sup(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2269]),
    [final] ).

cnf(i_0_3815,plain,
    ( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_sup_sup(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2270]),
    [final] ).

cnf(i_0_3816,plain,
    ( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_inf_inf(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2271]),
    [final] ).

cnf(i_0_3817,plain,
    ( hAPP(X2,X1,hAPP(fun(X2,X1),fun(X2,X1),hAPP(fun(X2,X1),fun(fun(X2,X1),fun(X2,X1)),semilattice_inf_inf(fun(X2,X1)),X3),X4),X5) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),hAPP(X2,X1,X3,X5)),hAPP(X2,X1,X4,X5))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2272]),
    [final] ).

cnf(i_0_3818,plain,
    ( X2 = X3
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2273]),
    [final] ).

cnf(i_0_3819,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_2274]),
    [final] ).

cnf(i_0_3820,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_2275]),
    [final] ).

cnf(i_0_3821,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_2276,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3822,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_2277,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3823,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_2278,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3824,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_2279,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3825,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_2280,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3826,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_2281,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3827,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))),X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2282]),
    [final] ).

cnf(i_0_3828,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),times_times(X1),X2),X2)))
    | ~ linordered_ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2283]),
    [final] ).

cnf(i_0_3829,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_2284]),
    [final] ).

cnf(i_0_3830,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_3831,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2286]),
    [final] ).

cnf(i_0_3832,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X4))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2287]),
    [final] ).

cnf(i_0_3833,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2288]),
    [final] ).

cnf(i_0_3834,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2289]),
    [final] ).

cnf(i_0_3835,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X4))
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2290]),
    [final] ).

cnf(i_0_3836,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_3837,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_2292]),
    [final] ).

cnf(i_0_3838,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,esk87_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_2228]),
    [final] ).

cnf(i_0_3839,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_3840,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2294]),
    [final] ).

cnf(i_0_3841,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2295]),
    [final] ).

cnf(i_0_3842,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)))
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2296]),
    [final] ).

cnf(i_0_3843,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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)),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2297,c_0_1517]),
    [final] ).

cnf(i_0_3844,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = 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)),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2298,c_0_1517]),
    [final] ).

cnf(i_0_3845,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),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)),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2299,c_0_1517]),
    [final] ).

cnf(i_0_3846,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),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_2300,c_0_1517]),
    [final] ).

cnf(i_0_3847,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),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_2301,c_0_1517]),
    [final] ).

cnf(i_0_3848,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_2302]),
    [final] ).

cnf(i_0_3849,plain,
    ( hAPP(fun(X1,bool),fun(nat,bool),hAPP(fun(X1,nat),fun(fun(X1,bool),fun(nat,bool)),image(X1,nat),esk122_2(X1,X2)),X2) = 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)),esk123_2(X1,X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2303]),
    [final] ).

cnf(i_0_3850,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_2304]),
    [final] ).

cnf(i_0_3851,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_2305]),
    [final] ).

cnf(i_0_3852,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_2306]),
    [final] ).

cnf(i_0_3853,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk177_3(X1,X2,X3)),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]),
    [final] ).

cnf(i_0_3854,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_2307]),
    [final] ).

cnf(i_0_3855,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_2308]),
    [final] ).

cnf(i_0_3856,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X1))),
    inference(split_conjunct,[status(thm)],[i_0_2309]),
    [final] ).

cnf(i_0_3857,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_2310]),
    [final] ).

cnf(i_0_3858,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_2311]),
    [final] ).

cnf(i_0_3859,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_2312]),
    [final] ).

cnf(i_0_3860,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_2313]),
    [final] ).

cnf(i_0_3861,plain,
    ( hBOOL(hAPP(arrow_1998540521e_indi,bool,hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool),arrow_708804735ctator,X1),X2))
    | hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),X1,esk18_2(X1,X2)) != hAPP(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),esk18_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1834]),
    [final] ).

cnf(i_0_3862,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_2314,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3863,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_2315,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3864,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_2316,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3865,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_2317,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3866,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_2318,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3867,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_2319,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3868,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_2320,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3869,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_2321,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3870,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_2322,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3871,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_2323,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3872,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_2324,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3873,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_2325,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3874,plain,
    ( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk80_2(X2,X3)))
    | ~ hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_3875,plain,
    ( hBOOL(hAPP(nat,bool,X3,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk82_2(X2,X3)))
    | ~ hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2326]),
    [final] ).

cnf(i_0_3876,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_2327]),
    [final] ).

cnf(i_0_3877,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_2328]),
    [final] ).

cnf(i_0_3878,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),esk70_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2329]),
    [final] ).

cnf(i_0_3879,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),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
    inference(rw,[status(thm)],[i_0_2330,c_0_1517]),
    [final] ).

cnf(i_0_3880,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_2331,c_0_1517]),
    [final] ).

cnf(i_0_3881,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk27_2(X1,X2)),arrow_1568854078le_Lin)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2332,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3882,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_2333]),
    [final] ).

cnf(i_0_3883,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_2334,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3884,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_2335]),
    [final] ).

cnf(i_0_3885,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),esk78_4(X2,X1,X3,X4)) != hAPP(X1,X1,combi(X1),esk77_4(X2,X1,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2336,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3886,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),esk32_4(X1,X2,X3,X4)) != hAPP(X1,X1,combi(X1),esk31_4(X1,X2,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2337,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3887,plain,
    hAPP(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)))),combi(fun(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))))),finite_fold_image(X1,X2)) = finite_fold_image(X1,X2),
    inference(rw,[status(thm)],[i_0_2338,c_0_1517]),
    [final] ).

cnf(i_0_3888,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk60_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_2232]),
    [final] ).

cnf(i_0_3889,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk94_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_2339]),
    [final] ).

cnf(i_0_3890,plain,
    ( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk88_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2340]),
    [final] ).

cnf(i_0_3891,plain,
    ( X2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk86_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2333]),
    [final] ).

cnf(i_0_3892,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_2231]),
    [final] ).

cnf(i_0_3893,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk174_3(X1,X2,X3)),X3))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_3894,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_2341]),
    [final] ).

cnf(i_0_3895,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_2229]),
    [final] ).

cnf(i_0_3896,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_1341]),
    [final] ).

cnf(i_0_3897,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_1342]),
    [final] ).

cnf(i_0_3898,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_2342,c_0_1517]),
    [final] ).

cnf(i_0_3899,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_2238]),
    [final] ).

cnf(i_0_3900,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_2207]),
    [final] ).

cnf(i_0_3901,plain,
    hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool)),combi(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,bool))),arrow_708804735ctator) = arrow_708804735ctator,
    inference(rw,[status(thm)],[i_0_2343,c_0_1517]),
    [final] ).

cnf(i_0_3902,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2344]),
    [final] ).

cnf(i_0_3903,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2345]),
    [final] ).

cnf(i_0_3904,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2346]),
    [final] ).

cnf(i_0_3905,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_2347]),
    [final] ).

cnf(i_0_3906,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_2348]),
    [final] ).

cnf(i_0_3907,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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_2349]),
    [final] ).

cnf(i_0_3908,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_2350]),
    [final] ).

cnf(i_0_3909,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_2351]),
    [final] ).

cnf(i_0_3910,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_2352]),
    [final] ).

cnf(i_0_3911,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_2353]),
    [final] ).

cnf(i_0_3912,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_2354]),
    [final] ).

cnf(i_0_3913,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_2355]),
    [final] ).

cnf(i_0_3914,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_2356]),
    [final] ).

cnf(i_0_3915,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_2352]),
    [final] ).

cnf(i_0_3916,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_2353]),
    [final] ).

cnf(i_0_3917,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_2357]),
    [final] ).

cnf(i_0_3918,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_2358,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3919,plain,
    hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),combi(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),arrow_1066301521nimity) = arrow_1066301521nimity,
    inference(rw,[status(thm)],[i_0_2359,c_0_1517]),
    [final] ).

cnf(i_0_3920,plain,
    hAPP(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),combi(fun(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),arrow_1541970350le_IIA) = arrow_1541970350le_IIA,
    inference(rw,[status(thm)],[i_0_2360,c_0_1517]),
    [final] ).

cnf(i_0_3921,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_2361]),
    [final] ).

cnf(i_0_3922,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk66_0),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_2362]),
    [final] ).

cnf(i_0_3923,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk20_0),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_2042]),
    [final] ).

cnf(i_0_3924,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),esk19_0),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[i_0_2043]),
    [final] ).

cnf(i_0_3925,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_36__096Lba_A_058_ALin_096]),
    [final] ).

cnf(i_0_3926,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab),arrow_1568854078le_Lin)),
    inference(split_conjunct,[status(thm)],[fact_35__096Lab_A_058_ALin_096]),
    [final] ).

cnf(i_0_3927,plain,
    ( hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,esk165_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1997]),
    [final] ).

cnf(i_0_3928,plain,
    ( hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,esk113_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1998]),
    [final] ).

cnf(i_0_3929,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk162_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3930,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk114_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1993]),
    [final] ).

cnf(i_0_3931,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk99_2(X2,X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_3932,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_2364,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3933,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_2365,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3934,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_2366,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3935,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_2367,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3936,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_2368,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3937,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_2369,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3938,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_2370,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3939,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_2143]),
    [final] ).

cnf(i_0_3940,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_2143]),
    [final] ).

cnf(i_0_3941,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk135_3(X1,X2,X3)),one_one(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linord1117847801e_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1827]),
    [final] ).

cnf(i_0_3942,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_2302]),
    [final] ).

cnf(i_0_3943,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_2371]),
    [final] ).

cnf(i_0_3944,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_2372]),
    [final] ).

cnf(i_0_3945,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_2373]),
    [final] ).

cnf(i_0_3946,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_2374]),
    [final] ).

cnf(i_0_3947,plain,
    ( hAPP(X2,X3,X4,hAPP(X1,X2,X5,X7)) = hAPP(X1,X3,X6,X7)
    | hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),comp(X2,X3,X1),X4),X5) != hAPP(fun(X1,X3),fun(X1,X3),combi(fun(X1,X3)),X6) ),
    inference(rw,[status(thm)],[i_0_2375,c_0_1517]),
    [final] ).

cnf(i_0_3948,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2376]),
    [final] ).

cnf(i_0_3949,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,combi(X1),X3)
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2377,c_0_1517]),
    [final] ).

cnf(i_0_3950,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,combi(X1),X3)
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2378,c_0_1517]),
    [final] ).

cnf(i_0_3951,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2) = hAPP(X1,X1,combi(X1),X3)
    | ~ semilattice_sup(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2379,c_0_1517]),
    [final] ).

cnf(i_0_3952,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2380,c_0_1517]),
    [final] ).

cnf(i_0_3953,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2381,c_0_1517]),
    [final] ).

cnf(i_0_3954,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(rw,[status(thm)],[i_0_2382,c_0_1517]),
    [final] ).

cnf(i_0_3955,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_2383,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3956,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_2384,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3957,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_2385,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3958,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_2386,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3959,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_2387]),
    [final] ).

cnf(i_0_3960,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_2388,c_0_1517]),c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3961,plain,
    ( hAPP(X1,X2,X3,esk77_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk78_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_1349]),
    [final] ).

cnf(i_0_3962,plain,
    ( hAPP(X1,X2,X3,esk31_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,esk32_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_1263]),
    [final] ).

cnf(i_0_3963,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk135_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linord1117847801e_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1827]),
    [final] ).

cnf(i_0_3964,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk100_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_2041]),
    [final] ).

cnf(i_0_3965,plain,
    ( hAPP(X1,nat,X2,esk175_3(X1,X2,X3)) = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]),
    [final] ).

cnf(i_0_3966,plain,
    hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combi(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),arrow_1665824030_below) = arrow_1665824030_below,
    inference(rw,[status(thm)],[i_0_2389,c_0_1517]),
    [final] ).

cnf(i_0_3967,plain,
    hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),combi(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))))),arrow_357225482_above) = arrow_357225482_above,
    inference(rw,[status(thm)],[i_0_2390,c_0_1517]),
    [final] ).

cnf(i_0_3968,plain,
    ( top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk149_2(X1,X2)),X2)) ),
    inference(rw,[status(thm)],[i_0_2391,c_0_1517]),
    [final] ).

cnf(i_0_3969,plain,
    hAPP(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)))),combi(fun(fun(X1,bool),fun(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3))))),compose(X1,X2,X3)) = compose(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_2392,c_0_1517]),
    [final] ).

cnf(i_0_3970,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_2393]),
    [final] ).

cnf(i_0_3971,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_2394,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3972,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_2395,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3973,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_2396,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3974,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_2397,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3975,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_2398,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3976,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_2399,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3977,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_2400,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3978,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) != hAPP(X1,X1,combi(X1),X3)
    | ~ semilattice_sup(X1) ),
    inference(rw,[status(thm)],[i_0_2401,c_0_1517]),
    [final] ).

cnf(i_0_3979,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1) ),
    inference(rw,[status(thm)],[i_0_2402,c_0_1517]),
    [final] ).

cnf(i_0_3980,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk83_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_2349]),
    [final] ).

cnf(i_0_3981,plain,
    ( X2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk56_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_2403]),
    [final] ).

cnf(i_0_3982,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_2404,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3983,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2405]),
    [final] ).

cnf(i_0_3984,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2406]),
    [final] ).

cnf(i_0_3985,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2407]),
    [final] ).

cnf(i_0_3986,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2408]),
    [final] ).

cnf(i_0_3987,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2409]),
    [final] ).

cnf(i_0_3988,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2410]),
    [final] ).

cnf(i_0_3989,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)
    | ~ ab_sem1668676832m_mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2411]),
    [final] ).

cnf(i_0_3990,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(X1,bool,X2,esk151_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_2412]),
    [final] ).

cnf(i_0_3991,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_2413]),
    [final] ).

cnf(i_0_3992,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_2414]),
    [final] ).

cnf(i_0_3993,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_2415]),
    [final] ).

cnf(i_0_3994,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_2264]),
    [final] ).

cnf(i_0_3995,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_2416]),
    [final] ).

cnf(i_0_3996,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_2417]),
    [final] ).

cnf(i_0_3997,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_2262]),
    [final] ).

cnf(i_0_3998,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_2418,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_3999,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_2419,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4000,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_2420,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4001,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_2421,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4002,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_2422,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4003,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_2423,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4004,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_2424,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4005,plain,
    hAPP(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool)),combi(fun(fun(X1,fun(X2,X2)),fun(fun(fun(X1,bool),fun(X2,X2)),bool))),finite_folding_idem(X1,X2)) = finite_folding_idem(X1,X2),
    inference(rw,[status(thm)],[i_0_2425,c_0_1517]),
    [final] ).

cnf(i_0_4006,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),esk72_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2250]),
    [final] ).

cnf(i_0_4007,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk74_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2251]),
    [final] ).

cnf(i_0_4008,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2426]),
    [final] ).

cnf(i_0_4009,plain,
    hAPP(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool))),combi(fun(fun(X1,nat),fun(fun(product_prod(X1,X1),bool),fun(product_prod(X1,X1),bool)))),mlex_prod(X1)) = mlex_prod(X1),
    inference(rw,[status(thm)],[i_0_2427,c_0_1517]),
    [final] ).

cnf(i_0_4010,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_2428]),
    [final] ).

cnf(i_0_4011,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_2429]),
    [final] ).

cnf(i_0_4012,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_2430,c_0_1517]),
    [final] ).

cnf(i_0_4013,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_2431]),
    [final] ).

cnf(i_0_4014,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_2432]),
    [final] ).

cnf(i_0_4015,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_2433]),
    [final] ).

cnf(i_0_4016,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk81_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_2434]),
    [final] ).

cnf(i_0_4017,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_2435]),
    [final] ).

cnf(i_0_4018,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_2436,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4019,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_2437,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4020,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_2438,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4021,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_2439,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4022,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_2440,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4023,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,esk21_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk21_4(X1,X2,X3,X4)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2441,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4024,plain,
    hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),hAPP(nat,nat,suc,X4)) = hAPP(nat,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_2442]),
    [final] ).

cnf(i_0_4025,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_2443,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4026,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_2444]),
    [final] ).

cnf(i_0_4027,plain,
    hAPP(nat,nat,size_size(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,size_size(nat),X1)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_2445]),
    [final] ).

cnf(i_0_4028,plain,
    ( X1 = hAPP(nat,nat,suc,esk94_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_2339]),
    [final] ).

cnf(i_0_4029,plain,
    hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,X1)),hAPP(nat,nat,suc,zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_2446]),
    [final] ).

cnf(i_0_4030,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,nat),fun(fun(X1,bool),bool),inj_on(X1,nat),esk122_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2303]),
    [final] ).

cnf(i_0_4031,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_2447,c_0_1517]),
    [final] ).

cnf(i_0_4032,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk82_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_2326]),
    [final] ).

cnf(i_0_4033,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk80_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_2254]),
    [final] ).

cnf(i_0_4034,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_2225]),
    [final] ).

cnf(i_0_4035,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_2448]),
    [final] ).

cnf(i_0_4036,plain,
    ( hAPP(X2,X2,combi(X2),X4) = hAPP(X1,X2,X3,esk129_4(X1,X2,X3,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_2449,c_0_1517]),
    [final] ).

cnf(i_0_4037,plain,
    ( hAPP(X2,X2,combi(X2),X4) = hAPP(X1,X2,X3,esk127_4(X1,X2,X4,X3))
    | 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_2450,c_0_1517]),
    [final] ).

cnf(i_0_4038,plain,
    ( hAPP(X2,X2,combi(X2),X4) = hAPP(X1,X2,X3,esk126_4(X1,X2,X4,X3))
    | 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_2451,c_0_1517]),
    [final] ).

cnf(i_0_4039,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_1371]),
    [final] ).

cnf(i_0_4040,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_2452,c_0_1517]),
    [final] ).

cnf(i_0_4041,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_2453,c_0_1517]),
    [final] ).

cnf(i_0_4042,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk29_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[i_0_1530]),
    [final] ).

cnf(i_0_4043,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[i_0_1531]),
    [final] ).

cnf(i_0_4044,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[fact_19_n_I1_J]),
    [final] ).

cnf(i_0_4045,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk151_3(X1,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(split_conjunct,[status(thm)],[i_0_2412]),
    [final] ).

cnf(i_0_4046,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_2403]),
    [final] ).

cnf(i_0_4047,plain,
    ( hAPP(X1,nat,X2,esk177_3(X1,X2,X3)) = one_one(nat)
    | hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1299]),
    [final] ).

cnf(i_0_4048,plain,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_1(X1))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2454]),
    [final] ).

cnf(i_0_4049,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2455]),
    [final] ).

cnf(i_0_4050,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2456]),
    [final] ).

cnf(i_0_4051,plain,
    ( X1 = hAPP(nat,nat,suc,esk89_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_2457]),
    [final] ).

cnf(i_0_4052,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_2458]),
    [final] ).

cnf(i_0_4053,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3)) = hAPP(X1,X1,combi(X1),X2)
    | ~ lattice(X1) ),
    inference(rw,[status(thm)],[i_0_2459,c_0_1517]),
    [final] ).

cnf(i_0_4054,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3)) = hAPP(X1,X1,combi(X1),X2)
    | ~ lattice(X1) ),
    inference(rw,[status(thm)],[i_0_2460,c_0_1517]),
    [final] ).

cnf(i_0_4055,plain,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_2461]),
    [final] ).

cnf(i_0_4056,plain,
    hAPP(fun(arrow_1998540521e_indi,bool),fun(nat,bool),hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),fun(nat,bool)),image(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_1998540521e_indi,bool),nat,finite_card(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_457_surjh]),
    [final] ).

cnf(i_0_4057,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_2462]),
    [final] ).

cnf(i_0_4058,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_2393]),
    [final] ).

cnf(i_0_4059,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_2463]),
    [final] ).

cnf(i_0_4060,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_2464]),
    [final] ).

cnf(i_0_4061,plain,
    hAPP(nat,X1,hAPP(fun(nat,X1),fun(nat,X1),hAPP(X1,fun(fun(nat,X1),fun(nat,X1)),nat_case(X1),X2),X3),zero_zero(nat)) = hAPP(X1,X1,combi(X1),X2),
    inference(rw,[status(thm)],[i_0_2465,c_0_1517]),
    [final] ).

cnf(i_0_4062,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_2466]),
    [final] ).

cnf(i_0_4063,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_2357]),
    [final] ).

cnf(i_0_4064,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_2467]),
    [final] ).

cnf(i_0_4065,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_2231]),
    [final] ).

cnf(i_0_4066,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_2237]),
    [final] ).

cnf(i_0_4067,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_2468]),
    [final] ).

cnf(i_0_4068,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2469]),
    [final] ).

cnf(i_0_4069,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_2470]),
    [final] ).

cnf(i_0_4070,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_2471]),
    [final] ).

cnf(i_0_4071,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_2472]),
    [final] ).

cnf(i_0_4072,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_2473]),
    [final] ).

cnf(i_0_4073,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[i_0_2474]),
    [final] ).

cnf(i_0_4074,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_2475]),
    [final] ).

cnf(i_0_4075,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2353]),
    [final] ).

cnf(i_0_4076,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2476]),
    [final] ).

cnf(i_0_4077,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2477]),
    [final] ).

cnf(i_0_4078,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2432]),
    [final] ).

cnf(i_0_4079,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2432]),
    [final] ).

cnf(i_0_4080,plain,
    ( X1 = X3
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2478]),
    [final] ).

cnf(i_0_4081,plain,
    ( X1 = zero_zero(nat)
    | X2 = X3
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2479]),
    [final] ).

cnf(i_0_4082,plain,
    ( X2 = X3
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2480]),
    [final] ).

cnf(i_0_4083,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2481]),
    [final] ).

cnf(i_0_4084,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2482]),
    [final] ).

cnf(i_0_4085,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_2483]),
    [final] ).

cnf(i_0_4086,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_2484]),
    [final] ).

cnf(i_0_4087,plain,
    hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),X2),
    inference(split_conjunct,[status(thm)],[i_0_2485]),
    [final] ).

cnf(i_0_4088,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2486]),
    [final] ).

cnf(i_0_4089,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2487]),
    [final] ).

cnf(i_0_4090,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2488]),
    [final] ).

cnf(i_0_4091,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(fun(X1,nat),fun(fun(X1,bool),nat),big_co1399186613setsum(X1,nat),X2),X3) = zero_zero(nat)
    | hAPP(X1,nat,X2,esk174_3(X1,X2,X3)) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_4092,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_2251]),
    [final] ).

cnf(i_0_4093,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk72_2(X1,X2)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2250]),
    [final] ).

cnf(i_0_4094,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2426]),
    [final] ).

cnf(i_0_4095,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_2489,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4096,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_2490,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4097,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_2491,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4098,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_2492,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4099,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_2493,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4100,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_2494,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4101,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_2495,c_0_1517]),
    [final] ).

cnf(i_0_4102,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_2496,c_0_1517]),
    [final] ).

cnf(i_0_4103,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_2497,c_0_1517]),
    [final] ).

cnf(i_0_4104,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_2498,c_0_1517]),
    [final] ).

cnf(i_0_4105,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_4106,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X3) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_4107,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_2428]),
    [final] ).

cnf(i_0_4108,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_2428]),
    [final] ).

cnf(i_0_4109,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_2501]),
    [final] ).

cnf(i_0_4110,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2502]),
    [final] ).

cnf(i_0_4111,plain,
    ( hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),hAPP(X1,fun(X2,X1),combk(X1,X2),zero_zero(X1))),X3) = zero_zero(X1)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2503]),
    [final] ).

cnf(i_0_4112,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_2504]),
    [final] ).

cnf(i_0_4113,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_2505,c_0_1517]),
    [final] ).

cnf(i_0_4114,plain,
    ( 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))) = top_top(fun(X1,bool))
    | hAPP(X1,X1,combi(X1),esk130_3(X2,X1,X3)) != hAPP(X2,X1,X3,X4) ),
    inference(rw,[status(thm)],[i_0_2506,c_0_1517]),
    [final] ).

cnf(i_0_4115,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_2507]),
    [final] ).

cnf(i_0_4116,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_2508]),
    [final] ).

cnf(i_0_4117,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_2509]),
    [final] ).

cnf(i_0_4118,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,esk98_1(X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2454]),
    [final] ).

cnf(i_0_4119,hypothesis,
    hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combi(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),f) = f,
    inference(rw,[status(thm)],[i_0_2510,c_0_1517]),
    [final] ).

cnf(i_0_4120,plain,
    hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combi(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1770777252_mktop) = arrow_1770777252_mktop,
    inference(rw,[status(thm)],[i_0_2511,c_0_1517]),
    [final] ).

cnf(i_0_4121,plain,
    hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),combi(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)))),arrow_1622070166_mkbot) = arrow_1622070166_mkbot,
    inference(rw,[status(thm)],[i_0_2512,c_0_1517]),
    [final] ).

cnf(i_0_4122,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_2513,c_0_1517]),
    [final] ).

cnf(i_0_4123,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_2514]),
    [final] ).

cnf(i_0_4124,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),esk101_0),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_2461]),
    [final] ).

cnf(i_0_4125,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,hAPP(fun(arrow_1998540521e_indi,nat),fun(fun(arrow_1998540521e_indi,bool),bool),inj_on(arrow_1998540521e_indi,nat),h),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_20_injh]),
    [final] ).

cnf(i_0_4126,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_2458]),
    [final] ).

cnf(i_0_4127,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk148_1(X1)),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_2515]),
    [final] ).

cnf(i_0_4128,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_2516]),
    [final] ).

cnf(i_0_4129,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_2517]),
    [final] ).

cnf(i_0_4130,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_2518,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4131,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_2519]),
    [final] ).

cnf(i_0_4132,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_2520,c_0_1517]),
    [final] ).

cnf(i_0_4133,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_2521]),
    [final] ).

cnf(i_0_4134,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_2522]),
    [final] ).

cnf(i_0_4135,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_2507]),
    [final] ).

cnf(i_0_4136,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_2507]),
    [final] ).

cnf(i_0_4137,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_2508]),
    [final] ).

cnf(i_0_4138,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_2508]),
    [final] ).

cnf(i_0_4139,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_2523]),
    [final] ).

cnf(i_0_4140,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_2523]),
    [final] ).

cnf(i_0_4141,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_2524]),
    [final] ).

cnf(i_0_4142,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk99_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_4143,plain,
    ( hBOOL(hAPP(nat,bool,X1,esk82_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2326]),
    [final] ).

cnf(i_0_4144,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[i_0_2523]),
    [final] ).

cnf(i_0_4145,plain,
    ( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2525,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4146,plain,
    ( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
    | ~ no_zero_divisors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2526,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4147,plain,
    ( hAPP(X1,X1,combi(X1),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) != zero_zero(X1)
    | ~ no_zero_divisors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2527,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4148,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_2524]),
    [final] ).

cnf(i_0_4149,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_2528,c_0_1517]),
    [final] ).

cnf(i_0_4150,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_2529,c_0_1517]),
    [final] ).

cnf(i_0_4151,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)))),comp(X1,X2,X3)) = comp(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_2530,c_0_1517]),
    [final] ).

cnf(i_0_4152,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_2531,c_0_1517]),
    [final] ).

cnf(i_0_4153,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_2532]),
    [final] ).

cnf(i_0_4154,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_2533]),
    [final] ).

cnf(i_0_4155,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = top_top(X1)
    | hAPP(X1,X1,combi(X1),X3) != top_top(X1)
    | hAPP(X1,X1,combi(X1),X2) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2534,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4156,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_2507]),
    [final] ).

cnf(i_0_4157,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_2508]),
    [final] ).

cnf(i_0_4158,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),top_top(fun(X1,bool))),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_2535,c_0_1517]),
    [final] ).

cnf(i_0_4159,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_2536,c_0_1517]),
    [final] ).

cnf(i_0_4160,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)))),the_inv_into(X1,X2)) = the_inv_into(X1,X2),
    inference(rw,[status(thm)],[i_0_2537,c_0_1517]),
    [final] ).

cnf(i_0_4161,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2538]),
    [final] ).

cnf(i_0_4162,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2539]),
    [final] ).

cnf(i_0_4163,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X3),X2)
    | ~ semilattice_sup(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2540]),
    [final] ).

cnf(i_0_4164,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2541]),
    [final] ).

cnf(i_0_4165,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2542]),
    [final] ).

cnf(i_0_4166,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2)
    | ~ semilattice_inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2543]),
    [final] ).

cnf(i_0_4167,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2544]),
    [final] ).

cnf(i_0_4168,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_2545]),
    [final] ).

cnf(i_0_4169,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_2546]),
    [final] ).

cnf(i_0_4170,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_2547]),
    [final] ).

cnf(i_0_4171,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_2548]),
    [final] ).

cnf(i_0_4172,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_2549]),
    [final] ).

cnf(i_0_4173,plain,
    hAPP(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2))),combi(fun(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)))),restrict(X1,X2)) = restrict(X1,X2),
    inference(rw,[status(thm)],[i_0_2550,c_0_1517]),
    [final] ).

cnf(i_0_4174,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_2551]),
    [final] ).

cnf(i_0_4175,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_2470]),
    [final] ).

cnf(i_0_4176,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_2552]),
    [final] ).

cnf(i_0_4177,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_2553]),
    [final] ).

cnf(i_0_4178,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_2471]),
    [final] ).

cnf(i_0_4179,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),X3,hAPP(fun(X1,X3),fun(fun(X1,bool),X3),big_co1399186613setsum(X1,X3),X4),X2) = zero_zero(X3)
    | ~ comm_monoid_add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1995]),
    [final] ).

cnf(i_0_4180,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X3) = zero_zero(X1)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2554]),
    [final] ).

cnf(i_0_4181,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | hAPP(fun(X2,bool),X1,hAPP(fun(X2,X1),fun(fun(X2,bool),X1),big_co1399186613setsum(X2,X1),X4),X3) = zero_zero(X1)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2555]),
    [final] ).

cnf(i_0_4182,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_2556,c_0_1517]),
    [final] ).

cnf(i_0_4183,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),top_top(fun(X1,bool))) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_2557,c_0_1517]),
    [final] ).

cnf(i_0_4184,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2479]),
    [final] ).

cnf(i_0_4185,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X3)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2480]),
    [final] ).

cnf(i_0_4186,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X3),X1)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2478]),
    [final] ).

cnf(i_0_4187,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_2355]),
    [final] ).

cnf(i_0_4188,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_2352]),
    [final] ).

cnf(i_0_4189,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_2558]),
    [final] ).

cnf(i_0_4190,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2559]),
    [final] ).

cnf(i_0_4191,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2560]),
    [final] ).

cnf(i_0_4192,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_2561]),
    [final] ).

cnf(i_0_4193,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2562]),
    [final] ).

cnf(i_0_4194,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2563]),
    [final] ).

cnf(i_0_4195,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2564]),
    [final] ).

cnf(i_0_4196,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_2565,c_0_1517]),
    [final] ).

cnf(i_0_4197,plain,
    ( hAPP(X1,X1,combi(X1),X2) = top_top(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X3) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(rw,[status(thm)],[i_0_2566,c_0_1517]),
    [final] ).

cnf(i_0_4198,plain,
    ( hAPP(X1,X1,combi(X1),X2) = top_top(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X3),X2) != top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(rw,[status(thm)],[i_0_2567,c_0_1517]),
    [final] ).

cnf(i_0_4199,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_2568,c_0_1517]),
    [final] ).

cnf(i_0_4200,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_2569,c_0_1517]),
    [final] ).

cnf(i_0_4201,plain,
    hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool),combi(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool)),arrow_301600364e_Prof) = arrow_301600364e_Prof,
    inference(rw,[status(thm)],[i_0_2570,c_0_1517]),
    [final] ).

cnf(i_0_4202,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_2571,c_0_1517]),
    [final] ).

cnf(i_0_4203,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_inf_inf(fun(X1,bool)),X2),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2),
    inference(rw,[status(thm)],[i_0_2572,c_0_1517]),
    [final] ).

cnf(i_0_4204,plain,
    ( hBOOL(hAPP(X1,bool,X2,esk146_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(X1,bool,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_4205,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_2573,c_0_1517]),
    [final] ).

cnf(i_0_4206,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_2574,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4207,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_2507]),
    [final] ).

cnf(i_0_4208,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_2507]),
    [final] ).

cnf(i_0_4209,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_2508]),
    [final] ).

cnf(i_0_4210,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_2508]),
    [final] ).

cnf(i_0_4211,plain,
    hAPP(nat,fun(nat,bool),ord_greaterThan(nat),zero_zero(nat)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),top_top(fun(nat,bool))),
    inference(split_conjunct,[status(thm)],[fact_531_greaterThan__0]),
    [final] ).

cnf(i_0_4212,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) != hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X3)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2575,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4213,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
    | hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) != hAPP(X1,fun(X1,bool),ord_atLeast(X1),X3)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2576,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4214,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1066301521nimity,f)),
    inference(split_conjunct,[status(thm)],[fact_1_u]),
    [final] ).

cnf(i_0_4215,plain,
    hBOOL(hAPP(fun(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),bool,arrow_1541970350le_IIA,f)),
    inference(split_conjunct,[status(thm)],[fact_0_assms_I3_J]),
    [final] ).

cnf(i_0_4216,plain,
    ( hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),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_2577,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4217,plain,
    ( hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),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_2578,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4218,plain,
    hAPP(fun(X1,fun(fun(nat,X1),fun(nat,X1))),fun(X1,fun(fun(nat,X1),fun(nat,X1))),combi(fun(X1,fun(fun(nat,X1),fun(nat,X1)))),nat_case(X1)) = nat_case(X1),
    inference(rw,[status(thm)],[i_0_2579,c_0_1517]),
    [final] ).

cnf(i_0_4219,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),top_top(fun(X1,bool))),X2) = top_top(fun(X1,bool)),
    inference(split_conjunct,[status(thm)],[i_0_2580]),
    [final] ).

cnf(i_0_4220,plain,
    hAPP(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),fun(product_prod(fun(X1,bool),fun(X1,bool)),bool),combi(fun(product_prod(fun(X1,bool),fun(X1,bool)),bool)),finite_psubset(X1)) = finite_psubset(X1),
    inference(rw,[status(thm)],[i_0_2581,c_0_1517]),
    [final] ).

cnf(i_0_4221,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool)),
    inference(split_conjunct,[status(thm)],[i_0_2582]),
    [final] ).

cnf(i_0_4222,plain,
    ( X1 = zero_zero(nat)
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2583]),
    [final] ).

cnf(i_0_4223,plain,
    ( X2 = one_one(nat)
    | X1 = zero_zero(nat)
    | X1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2584]),
    [final] ).

cnf(i_0_4224,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_2585]),
    [final] ).

cnf(i_0_4225,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_2585]),
    [final] ).

cnf(i_0_4226,plain,
    ( X1 = one_one(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) != one_one(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2586]),
    [final] ).

cnf(i_0_4227,plain,
    ( X1 = one_one(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) != one_one(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2586]),
    [final] ).

cnf(i_0_4228,plain,
    ( X1 = one_one(nat)
    | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2587]),
    [final] ).

cnf(i_0_4229,plain,
    ( X1 = one_one(nat)
    | one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2587]),
    [final] ).

cnf(i_0_4230,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_2588]),
    [final] ).

cnf(i_0_4231,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(rw,[status(thm)],[i_0_2589,c_0_1517]),
    [final] ).

cnf(i_0_4232,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X2) = zero_zero(X1)
    | hAPP(X1,X1,combi(X1),X2) != zero_zero(X1)
    | ~ ring_n68954251visors(X1) ),
    inference(rw,[status(thm)],[i_0_2590,c_0_1517]),
    [final] ).

cnf(i_0_4233,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_2591,c_0_1517]),
    [final] ).

cnf(i_0_4234,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_2592,c_0_1517]),
    [final] ).

cnf(i_0_4235,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_2593,c_0_1517]),
    [final] ).

cnf(i_0_4236,plain,
    ( hAPP(fun(fun(X2,X1),fun(fun(X2,bool),X1)),fun(fun(X2,X1),fun(fun(X2,bool),X1)),combi(fun(fun(X2,X1),fun(fun(X2,bool),X1))),big_co1399186613setsum(X2,X1)) = big_co1399186613setsum(X2,X1)
    | ~ comm_monoid_add(X1) ),
    inference(rw,[status(thm)],[i_0_2594,c_0_1517]),
    [final] ).

cnf(i_0_4237,plain,
    hAPP(fun(fun(X1,bool),fun(fun(X1,X2),bool)),fun(fun(X1,bool),fun(fun(X1,X2),bool)),combi(fun(fun(X1,bool),fun(fun(X1,X2),bool))),extensional(X1,X2)) = extensional(X1,X2),
    inference(rw,[status(thm)],[i_0_2595,c_0_1517]),
    [final] ).

cnf(i_0_4238,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_2596,c_0_1517]),
    [final] ).

cnf(i_0_4239,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_2434]),
    [final] ).

cnf(i_0_4240,plain,
    hAPP(fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),fun(fun(X1,nat),fun(product_prod(X1,X1),bool)),combi(fun(fun(X1,nat),fun(product_prod(X1,X1),bool))),measure(X1)) = measure(X1),
    inference(rw,[status(thm)],[i_0_2597,c_0_1517]),
    [final] ).

cnf(i_0_4241,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_2598,c_0_1517]),
    [final] ).

cnf(i_0_4242,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),top_top(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ bounded_lattice_top(X1) ),
    inference(rw,[status(thm)],[i_0_2599,c_0_1517]),
    [final] ).

cnf(i_0_4243,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_monoid_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2600,c_0_1517]),
    [final] ).

cnf(i_0_4244,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_semiring_1(X1) ),
    inference(rw,[status(thm)],[i_0_2601,c_0_1517]),
    [final] ).

cnf(i_0_4245,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),one_one(X1)),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ monoid_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2602,c_0_1517]),
    [final] ).

cnf(i_0_4246,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_2603,c_0_1517]),
    [final] ).

cnf(i_0_4247,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_2604,c_0_1517]),
    [final] ).

cnf(i_0_4248,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_2605,c_0_1517]),
    [final] ).

cnf(i_0_4249,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),top_top(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ bounded_lattice_top(X1) ),
    inference(rw,[status(thm)],[i_0_2606,c_0_1517]),
    [final] ).

cnf(i_0_4250,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_monoid_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2607,c_0_1517]),
    [final] ).

cnf(i_0_4251,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ comm_semiring_1(X1) ),
    inference(rw,[status(thm)],[i_0_2608,c_0_1517]),
    [final] ).

cnf(i_0_4252,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),one_one(X1)) = hAPP(X1,X1,combi(X1),X2)
    | ~ monoid_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2609,c_0_1517]),
    [final] ).

cnf(i_0_4253,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_2610,c_0_1517]),
    [final] ).

cnf(i_0_4254,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_2611,c_0_1517]),
    [final] ).

cnf(i_0_4255,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_2612,c_0_1517]),
    [final] ).

cnf(i_0_4256,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ lattice(X1) ),
    inference(rw,[status(thm)],[i_0_2613,c_0_1517]),
    [final] ).

cnf(i_0_4257,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_sup(X1) ),
    inference(rw,[status(thm)],[i_0_2614,c_0_1517]),
    [final] ).

cnf(i_0_4258,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_sup(X1) ),
    inference(rw,[status(thm)],[i_0_2615,c_0_1517]),
    [final] ).

cnf(i_0_4259,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ lattice(X1) ),
    inference(rw,[status(thm)],[i_0_2616,c_0_1517]),
    [final] ).

cnf(i_0_4260,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1) ),
    inference(rw,[status(thm)],[i_0_2617,c_0_1517]),
    [final] ).

cnf(i_0_4261,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_inf_inf(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ semilattice_inf(X1) ),
    inference(rw,[status(thm)],[i_0_2618,c_0_1517]),
    [final] ).

cnf(i_0_4262,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ ab_sem1668676832m_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2619,c_0_1517]),
    [final] ).

cnf(i_0_4263,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2) = hAPP(X1,X1,combi(X1),X2)
    | ~ ab_sem1668676832m_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2620,c_0_1517]),
    [final] ).

cnf(i_0_4264,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_2621]),
    [final] ).

cnf(i_0_4265,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_2622]),
    [final] ).

cnf(i_0_4266,plain,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),X1),
    inference(split_conjunct,[status(thm)],[i_0_2623]),
    [final] ).

cnf(i_0_4267,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_2624]),
    [final] ).

cnf(i_0_4268,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_2625,c_0_1517]),
    [final] ).

cnf(i_0_4269,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_2626,c_0_1517]),c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4270,plain,
    hAPP(X1,X2,X3,hAPP(X1,X1,combi(X1),X4)) = hAPP(X1,X2,X3,X4),
    inference(rw,[status(thm)],[i_0_2627,c_0_1517]),
    [final] ).

cnf(i_0_4271,plain,
    hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(rw,[status(thm)],[i_0_2628,c_0_1517]),
    [final] ).

cnf(i_0_4272,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(split_conjunct,[status(thm)],[i_0_2629]),
    [final] ).

cnf(i_0_4273,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_2630,c_0_1517]),
    [final] ).

cnf(i_0_4274,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_gr676655987ssThan(X1)) = ord_gr676655987ssThan(X1)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[i_0_2631,c_0_1517]),
    [final] ).

cnf(i_0_4275,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_gr1471790799AtMost(X1)) = ord_gr1471790799AtMost(X1)
    | ~ linorder(X1) ),
    inference(rw,[status(thm)],[i_0_2632,c_0_1517]),
    [final] ).

cnf(i_0_4276,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_2633,c_0_1517]),
    [final] ).

cnf(i_0_4277,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_atLeastAtMost(X1)) = ord_atLeastAtMost(X1)
    | ~ order(X1) ),
    inference(rw,[status(thm)],[i_0_2634,c_0_1517]),
    [final] ).

cnf(i_0_4278,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_2635,c_0_1517]),
    [final] ).

cnf(i_0_4279,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_2636]),
    [final] ).

cnf(i_0_4280,plain,
    hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),combi(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool)),arrow_1568854078le_Lin) = arrow_1568854078le_Lin,
    inference(rw,[status(thm)],[i_0_2637,c_0_1517]),
    [final] ).

cnf(i_0_4281,hypothesis,
    hAPP(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),combi(fun(arrow_1998540521e_indi,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),p) = p,
    inference(rw,[status(thm)],[i_0_2638,c_0_1517]),
    [final] ).

cnf(i_0_4282,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_1968]),
    [final] ).

cnf(i_0_4283,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_2639]),
    [final] ).

cnf(i_0_4284,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),top_top(X1)),X2) = top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2640]),
    [final] ).

cnf(i_0_4285,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2641]),
    [final] ).

cnf(i_0_4286,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),zero_zero(X1)),X2) = zero_zero(X1)
    | ~ mult_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2642]),
    [final] ).

cnf(i_0_4287,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),semilattice_sup_sup(X1),X2),top_top(X1)) = top_top(X1)
    | ~ bounded_lattice_top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2643]),
    [final] ).

cnf(i_0_4288,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2644]),
    [final] ).

cnf(i_0_4289,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),zero_zero(X1)) = zero_zero(X1)
    | ~ mult_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2645]),
    [final] ).

cnf(i_0_4290,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = one_one(nat)
    | X1 != one_one(nat)
    | X2 != one_one(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2586]),
    [final] ).

cnf(i_0_4291,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_2585]),
    [final] ).

cnf(i_0_4292,plain,
    ( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2)
    | X1 != one_one(nat)
    | X2 != one_one(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2587]),
    [final] ).

cnf(i_0_4293,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_2646]),
    [final] ).

cnf(i_0_4294,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),X2) = zero_zero(nat)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2583]),
    [final] ).

cnf(i_0_4295,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),X1) = zero_zero(nat)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[i_0_2583]),
    [final] ).

cnf(i_0_4296,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2647]),
    [final] ).

cnf(i_0_4297,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2648]),
    [final] ).

cnf(i_0_4298,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ),
    inference(rw,[status(thm)],[i_0_2649,c_0_1517]),
    [final] ).

cnf(i_0_4299,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_2650]),
    [final] ).

cnf(i_0_4300,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),one_one(nat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2651]),
    [final] ).

cnf(i_0_4301,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2652]),
    [final] ).

cnf(i_0_4302,plain,
    ( ~ hBOOL(hAPP(bool,bool,fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2653]),
    [final] ).

cnf(i_0_4303,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2654]),
    [final] ).

cnf(i_0_4304,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2655]),
    [final] ).

cnf(i_0_4305,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_2656,c_0_1517]),
    [final] ).

cnf(i_0_4306,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_2657]),
    [final] ).

cnf(i_0_4307,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_2658,c_0_1517]),
    [final] ).

cnf(i_0_4308,plain,
    hBOOL(hAPP(fun(arrow_1998540521e_indi,bool),bool,finite_finite_1(arrow_1998540521e_indi),top_top(fun(arrow_1998540521e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[fact_276_finite__indi]),
    [final] ).

cnf(i_0_4309,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_2659,c_0_1517]),
    [final] ).

cnf(i_0_4310,plain,
    hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2660]),
    [final] ).

cnf(i_0_4311,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),semilattice_sup_sup(X1)) = semilattice_sup_sup(X1)
    | ~ semilattice_sup(X1) ),
    inference(rw,[status(thm)],[i_0_2661,c_0_1517]),
    [final] ).

cnf(i_0_4312,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),semilattice_inf_inf(X1)) = semilattice_inf_inf(X1)
    | ~ semilattice_inf(X1) ),
    inference(rw,[status(thm)],[i_0_2662,c_0_1517]),
    [final] ).

cnf(i_0_4313,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
    | ~ no_zero_divisors(X1) ),
    inference(rw,[status(thm)],[i_0_2663,c_0_1517]),
    [final] ).

cnf(i_0_4314,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
    | ~ mult_zero(X1) ),
    inference(rw,[status(thm)],[i_0_2664,c_0_1517]),
    [final] ).

cnf(i_0_4315,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
    | ~ ab_semigroup_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2665,c_0_1517]),
    [final] ).

cnf(i_0_4316,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
    | ~ monoid_mult(X1) ),
    inference(rw,[status(thm)],[i_0_2666,c_0_1517]),
    [final] ).

cnf(i_0_4317,plain,
    ( hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(X1,X1)),combi(fun(X1,fun(X1,X1))),times_times(X1)) = times_times(X1)
    | ~ semiring(X1) ),
    inference(rw,[status(thm)],[i_0_2667,c_0_1517]),
    [final] ).

cnf(i_0_4318,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_2668,c_0_1517]),
    [final] ).

cnf(i_0_4319,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_2669,c_0_1517]),
    [final] ).

cnf(i_0_4320,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_2670,c_0_1517]),
    [final] ).

cnf(i_0_4321,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2671]),
    [final] ).

cnf(i_0_4322,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2672]),
    [final] ).

cnf(i_0_4323,plain,
    ( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_greaterThan(X1)) = ord_greaterThan(X1)
    | ~ ord(X1) ),
    inference(rw,[status(thm)],[i_0_2673,c_0_1517]),
    [final] ).

cnf(i_0_4324,plain,
    ( hAPP(fun(X1,fun(X1,bool)),fun(X1,fun(X1,bool)),combi(fun(X1,fun(X1,bool))),ord_atLeast(X1)) = ord_atLeast(X1)
    | ~ ord(X1) ),
    inference(rw,[status(thm)],[i_0_2674,c_0_1517]),
    [final] ).

cnf(i_0_4325,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_2675,c_0_1517]),
    [final] ).

cnf(i_0_4326,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_2676,c_0_1517]),
    [final] ).

cnf(i_0_4327,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_2677,c_0_1517]),
    [final] ).

cnf(i_0_4328,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_2678,c_0_1517]),
    [final] ).

cnf(i_0_4329,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_2679,c_0_1517]),
    [final] ).

cnf(i_0_4330,hypothesis,
    ( hBOOL(hAPP(bool,bool,combi(bool),X1))
    | ~ hBOOL(X1) ),
    inference(rw,[status(thm)],[i_0_2680,c_0_1517]),
    [final] ).

cnf(i_0_4331,plain,
    hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),combi(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lba) = lba,
    inference(rw,[status(thm)],[i_0_2681,c_0_1517]),
    [final] ).

cnf(i_0_4332,plain,
    hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),combi(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),lab) = lab,
    inference(rw,[status(thm)],[i_0_2682,c_0_1517]),
    [final] ).

cnf(i_0_4333,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_2683,c_0_1517]),
    [final] ).

cnf(i_0_4334,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_2684,c_0_1517]),
    [final] ).

cnf(i_0_4335,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_2685,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4336,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_2686,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4337,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_2687,c_0_1517]),c_0_1517]),
    [final] ).

cnf(i_0_4338,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(bool,bool,fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2688]),
    [final] ).

cnf(i_0_4339,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_2689]),
    [final] ).

cnf(i_0_4340,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_2690]),
    [final] ).

cnf(i_0_4341,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[i_0_2691]),
    [final] ).

cnf(i_0_4342,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2692]),
    [final] ).

cnf(i_0_4343,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2693]),
    [final] ).

cnf(i_0_4344,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2694]),
    [final] ).

cnf(i_0_4345,plain,
    hAPP(nat,nat,suc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_2695]),
    [final] ).

cnf(i_0_4346,plain,
    X1 != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[i_0_2696]),
    [final] ).

cnf(i_0_4347,plain,
    hAPP(fun(X1,X1),fun(X1,X1),combi(fun(X1,X1)),combi(X1)) = combi(X1),
    inference(rw,[status(thm)],[i_0_2697,c_0_1517]),
    [final] ).

cnf(i_0_4348,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_2698,c_0_1517]),
    [final] ).

cnf(i_0_4349,plain,
    hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),size_size(nat)) = size_size(nat),
    inference(rw,[status(thm)],[i_0_2699,c_0_1517]),
    [final] ).

cnf(i_0_4350,plain,
    hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),nat_size) = nat_size,
    inference(rw,[status(thm)],[i_0_2700,c_0_1517]),
    [final] ).

cnf(i_0_4351,plain,
    hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) = suc,
    inference(rw,[status(thm)],[i_0_2701,c_0_1517]),
    [final] ).

cnf(i_0_4352,plain,
    hAPP(fun(bool,nat),fun(bool,nat),combi(fun(bool,nat)),bool_size) = bool_size,
    inference(rw,[status(thm)],[i_0_2702,c_0_1517]),
    [final] ).

cnf(i_0_4353,plain,
    hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) = fNot,
    inference(rw,[status(thm)],[i_0_2703,c_0_1517]),
    [final] ).

cnf(i_0_4354,plain,
    hAPP(fun(arrow_1998540521e_indi,nat),fun(arrow_1998540521e_indi,nat),combi(fun(arrow_1998540521e_indi,nat)),h) = h,
    inference(rw,[status(thm)],[i_0_2704,c_0_1517]),
    [final] ).

cnf(i_0_4355,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_289_card__UNIV__unit]),
    [final] ).

cnf(i_0_4356,plain,
    ( hAPP(X2,X1,top_top(fun(X2,X1)),X3) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2705]),
    [final] ).

cnf(i_0_4357,plain,
    hAPP(nat,fun(nat,bool),ord_atLeast(nat),zero_zero(nat)) = top_top(fun(nat,bool)),
    inference(split_conjunct,[status(thm)],[fact_863_atLeast__0]),
    [final] ).

cnf(i_0_4358,plain,
    ( hAPP(X1,X1,combi(X1),top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(rw,[status(thm)],[i_0_2706,c_0_1517]),
    [final] ).

cnf(i_0_4359,plain,
    ( hAPP(X1,X1,combi(X1),zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(rw,[status(thm)],[i_0_2707,c_0_1517]),
    [final] ).

cnf(i_0_4360,plain,
    ( hAPP(X1,X1,combi(X1),one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(rw,[status(thm)],[i_0_2708,c_0_1517]),
    [final] ).

cnf(i_0_4361,plain,
    hAPP(X1,X1,combi(X1),undefined(X1)) = undefined(X1),
    inference(rw,[status(thm)],[i_0_2709,c_0_1517]),
    [final] ).

cnf(i_0_4362,plain,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,esk97_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2710]),
    [final] ).

cnf(i_0_4363,plain,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,esk96_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2711]),
    [final] ).

cnf(i_0_4364,plain,
    hAPP(nat,nat,size_size(nat),zero_zero(nat)) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[fact_743_nat_Osize_I3_J]),
    [final] ).

cnf(i_0_4365,plain,
    hAPP(nat,nat,nat_size,zero_zero(nat)) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[fact_727_nat_Osize_I1_J]),
    [final] ).

cnf(i_0_4366,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(split_conjunct,[status(thm)],[fact_423_One__nat__def]),
    [final] ).

cnf(i_0_4367,plain,
    hAPP(nat,nat,size_size(nat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2712]),
    [final] ).

cnf(i_0_4368,plain,
    hAPP(nat,nat,combi(nat),n) = n,
    inference(rw,[status(thm)],[i_0_2713,c_0_1517]),
    [final] ).

cnf(i_0_4369,plain,
    hAPP(bool,bool,combi(bool),fTrue) = fTrue,
    inference(rw,[status(thm)],[i_0_2714,c_0_1517]),
    [final] ).

cnf(i_0_4370,plain,
    hAPP(bool,bool,combi(bool),fFalse) = fFalse,
    inference(rw,[status(thm)],[i_0_2715,c_0_1517]),
    [final] ).

cnf(i_0_4371,plain,
    hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),e) = e,
    inference(rw,[status(thm)],[i_0_2716,c_0_1517]),
    [final] ).

cnf(i_0_4372,hypothesis,
    hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),d) = d,
    inference(rw,[status(thm)],[i_0_2717,c_0_1517]),
    [final] ).

cnf(i_0_4373,hypothesis,
    hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),c) = c,
    inference(rw,[status(thm)],[i_0_2718,c_0_1517]),
    [final] ).

cnf(i_0_4374,plain,
    hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),b) = b,
    inference(rw,[status(thm)],[i_0_2719,c_0_1517]),
    [final] ).

cnf(i_0_4375,plain,
    hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),a) = a,
    inference(rw,[status(thm)],[i_0_2720,c_0_1517]),
    [final] ).

cnf(i_0_4376,plain,
    hAPP(bool,nat,bool_size,fTrue) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[fact_755_bool_Osize_I1_J]),
    [final] ).

cnf(i_0_4377,plain,
    hAPP(bool,nat,bool_size,fFalse) = zero_zero(nat),
    inference(split_conjunct,[status(thm)],[fact_756_bool_Osize_I2_J]),
    [final] ).

cnf(i_0_4378,plain,
    ( finite_finite(sum_sum(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2721]),
    [final] ).

cnf(i_0_4379,plain,
    ( finite_finite(fun(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2722]),
    [final] ).

cnf(i_0_4380,plain,
    ( finite_finite(product_prod(X2,X1))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2723]),
    [final] ).

cnf(i_0_4381,plain,
    ( bounded_lattice(fun(X2,X1))
    | ~ bounded_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2724]),
    [final] ).

cnf(i_0_4382,plain,
    ( distrib_lattice(fun(X2,X1))
    | ~ distrib_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2725]),
    [final] ).

cnf(i_0_4383,plain,
    ( bounded_lattice_top(fun(X2,X1))
    | ~ bounded_lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2726]),
    [final] ).

cnf(i_0_4384,plain,
    ( lattice(fun(X2,X1))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2727]),
    [final] ).

cnf(i_0_4385,plain,
    ( preorder(fun(X2,X1))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2728]),
    [final] ).

cnf(i_0_4386,plain,
    ( order(fun(X2,X1))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2729]),
    [final] ).

cnf(i_0_4387,plain,
    ( top(fun(X2,X1))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2730]),
    [final] ).

cnf(i_0_4388,plain,
    ( ord(fun(X2,X1))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2731]),
    [final] ).

cnf(i_0_4389,plain,
    ( semilattice_sup(fun(X2,X1))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2732]),
    [final] ).

cnf(i_0_4390,plain,
    ( semilattice_inf(fun(X2,X1))
    | ~ lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2733]),
    [final] ).

cnf(i_0_4391,plain,
    ( ~ zero_neq_one(X1)
    | one_one(X1) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2734]),
    [final] ).

cnf(i_0_4392,plain,
    ( ~ zero_neq_one(X1)
    | zero_zero(X1) != one_one(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2735]),
    [final] ).

cnf(i_0_4393,plain,
    ( finite_finite(option(X1))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2736]),
    [final] ).

cnf(i_0_4394,plain,
    ~ hBOOL(fFalse),
    inference(split_conjunct,[status(thm)],[i_0_2737]),
    [final] ).

cnf(i_0_4395,plain,
    bounded_lattice(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Obounded__lattice]),
    [final] ).

cnf(i_0_4396,plain,
    semiring_0(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Osemiring__0]),
    [final] ).

cnf(i_0_4397,plain,
    distrib_lattice(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_4398,plain,
    distrib_lattice(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_4399,plain,
    bounded_lattice_top(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Obounded__lattice__top]),
    [final] ).

cnf(i_0_4400,plain,
    lattice(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Lattices_Olattice]),
    [final] ).

cnf(i_0_4401,plain,
    lattice(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Olattice]),
    [final] ).

cnf(i_0_4402,plain,
    linordered_semiring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_4403,plain,
    linord893533164strict(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict]),
    [final] ).

cnf(i_0_4404,plain,
    linord20386208strict(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semiring__strict]),
    [final] ).

cnf(i_0_4405,plain,
    ordere1490568538miring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__comm__semiring]),
    [final] ).

cnf(i_0_4406,plain,
    ordered_semiring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_4407,plain,
    ordere453448008miring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Oordered__cancel__semiring]),
    [final] ).

cnf(i_0_4408,plain,
    comm_semiring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4409,plain,
    comm_monoid_mult(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__mult]),
    [final] ).

cnf(i_0_4410,plain,
    semiri456707255roduct(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc]),
    [final] ).

cnf(i_0_4411,plain,
    comm_semiring_1(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_4412,plain,
    ordere216010020id_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_4413,plain,
    zero_neq_one(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_4414,plain,
    finite_finite(product_unit),
    inference(split_conjunct,[status(thm)],[arity_Product__Type_Ounit___Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_4415,plain,
    finite_finite(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_4416,plain,
    ordere779506340up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_4417,plain,
    ordere236663937imp_le(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_4418,plain,
    cancel146912293up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_4419,plain,
    ordere223160158up_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_4420,plain,
    linordered_semidom(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4421,plain,
    preorder(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]),
    [final] ).

cnf(i_0_4422,plain,
    preorder(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]),
    [final] ).

cnf(i_0_4423,plain,
    hBOOL(fTrue),
    inference(split_conjunct,[status(thm)],[help_fTrue_1_1_U]),
    [final] ).

cnf(i_0_4424,plain,
    linorder(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]),
    [final] ).

cnf(i_0_4425,plain,
    order(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]),
    [final] ).

cnf(i_0_4426,plain,
    order(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]),
    [final] ).

cnf(i_0_4427,plain,
    top(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Otop]),
    [final] ).

cnf(i_0_4428,plain,
    ord(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Orderings_Oord]),
    [final] ).

cnf(i_0_4429,plain,
    ord(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Oord]),
    [final] ).

cnf(i_0_4430,plain,
    semilattice_sup(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_4431,plain,
    semilattice_sup(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_4432,plain,
    semilattice_inf(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_4433,plain,
    semilattice_inf(bool),
    inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_4434,plain,
    zero(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ozero]),
    [final] ).

cnf(i_0_4435,plain,
    no_zero_divisors(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Ono__zero__divisors]),
    [final] ).

cnf(i_0_4436,plain,
    mult_zero(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Omult__zero]),
    [final] ).

cnf(i_0_4437,plain,
    ab_semigroup_mult(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__mult]),
    [final] ).

cnf(i_0_4438,plain,
    monoid_mult(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4439,plain,
    semiring(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Rings_Osemiring]),
    [final] ).

cnf(i_0_4440,plain,
    cancel_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_4441,plain,
    ab_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_4442,plain,
    monoid_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4443,plain,
    one(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Oone]),
    [final] ).

cnf(i_0_4444,plain,
    comm_monoid_add(nat),
    inference(split_conjunct,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_4445,plain,
    c != d,
    inference(split_conjunct,[status(thm)],[fact_2__096c_A_126_061_Ad_096]),
    [final] ).

cnf(i_0_4446,plain,
    a != b,
    inference(split_conjunct,[status(thm)],[fact_37__096a_A_126_061_Ab_096]),
    [final] ).

cnf(i_0_4447,axiom,
    X1 = X1 ).

cnf(i_0_4448,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4449,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4450,axiom,
    ( X1 != X2
    | hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).

cnf(i_0_4451,axiom,
    ( X1 != X2
    | hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).

cnf(i_0_4452,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).

cnf(i_0_4453,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).

cnf(i_0_4454,axiom,
    ( X1 != X2
    | times_times(X1) = times_times(X2) ) ).

cnf(i_0_4455,axiom,
    ( X1 != X2
    | top_top(X1) = top_top(X2) ) ).

cnf(i_0_4456,axiom,
    ( X1 != X2
    | extensional(X1,X3) = extensional(X2,X3) ) ).

cnf(i_0_4457,axiom,
    ( X1 != X2
    | extensional(X3,X1) = extensional(X3,X2) ) ).

cnf(i_0_4458,axiom,
    ( X1 != X2
    | finite_psubset(X1) = finite_psubset(X2) ) ).

cnf(i_0_4459,axiom,
    ( X1 != X2
    | ord_atLeastLessThan(X1) = ord_atLeastLessThan(X2) ) ).

cnf(i_0_4460,axiom,
    ( X1 != X2
    | ord_gr676655987ssThan(X1) = ord_gr676655987ssThan(X2) ) ).

cnf(i_0_4461,axiom,
    ( X1 != X2
    | ord_gr1471790799AtMost(X1) = ord_gr1471790799AtMost(X2) ) ).

cnf(i_0_4462,axiom,
    ( X1 != X2
    | measure(X1) = measure(X2) ) ).

cnf(i_0_4463,axiom,
    ( X1 != X2
    | in_rel(X1,X3) = in_rel(X2,X3) ) ).

cnf(i_0_4464,axiom,
    ( X1 != X2
    | in_rel(X3,X1) = in_rel(X3,X2) ) ).

cnf(i_0_4465,axiom,
    ( X1 != X2
    | finite_folding_idem(X1,X3) = finite_folding_idem(X2,X3) ) ).

cnf(i_0_4466,axiom,
    ( X1 != X2
    | finite_folding_idem(X3,X1) = finite_folding_idem(X3,X2) ) ).

cnf(i_0_4467,axiom,
    ( X1 != X2
    | nat_case(X1) = nat_case(X2) ) ).

cnf(i_0_4468,axiom,
    ( X1 != X2
    | sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).

cnf(i_0_4469,axiom,
    ( X1 != X2
    | sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).

cnf(i_0_4470,axiom,
    ( X1 != X2
    | ord_greaterThan(X1) = ord_greaterThan(X2) ) ).

cnf(i_0_4471,axiom,
    ( X1 != X2
    | ord_atLeast(X1) = ord_atLeast(X2) ) ).

cnf(i_0_4472,axiom,
    ( X1 != X2
    | product_Pair(X1,X3) = product_Pair(X2,X3) ) ).

cnf(i_0_4473,axiom,
    ( X1 != X2
    | product_Pair(X3,X1) = product_Pair(X3,X2) ) ).

cnf(i_0_4474,axiom,
    ( X1 != X2
    | combc(X1,X3,X4) = combc(X2,X3,X4) ) ).

cnf(i_0_4475,axiom,
    ( X1 != X2
    | combc(X3,X1,X4) = combc(X3,X2,X4) ) ).

cnf(i_0_4476,axiom,
    ( X1 != X2
    | combc(X3,X4,X1) = combc(X3,X4,X2) ) ).

cnf(i_0_4477,axiom,
    ( X1 != X2
    | product_prod_rec(X1,X3,X4) = product_prod_rec(X2,X3,X4) ) ).

cnf(i_0_4478,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X1,X4) = product_prod_rec(X3,X2,X4) ) ).

cnf(i_0_4479,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X4,X1) = product_prod_rec(X3,X4,X2) ) ).

cnf(i_0_4480,axiom,
    ( X1 != X2
    | combb(X1,X3,X4) = combb(X2,X3,X4) ) ).

cnf(i_0_4481,axiom,
    ( X1 != X2
    | combb(X3,X1,X4) = combb(X3,X2,X4) ) ).

cnf(i_0_4482,axiom,
    ( X1 != X2
    | combb(X3,X4,X1) = combb(X3,X4,X2) ) ).

cnf(i_0_4483,axiom,
    ( X1 != X2
    | size_size(X1) = size_size(X2) ) ).

cnf(i_0_4484,axiom,
    ( X1 != X2
    | if(X1) = if(X2) ) ).

cnf(i_0_4485,axiom,
    ( X1 != X2
    | undefined(X1) = undefined(X2) ) ).

cnf(i_0_4486,axiom,
    ( X1 != X2
    | ord_less(X1) = ord_less(X2) ) ).

cnf(i_0_4487,axiom,
    ( X1 != X2
    | plus_plus(X1) = plus_plus(X2) ) ).

cnf(i_0_4488,axiom,
    ( X1 != X2
    | one_one(X1) = one_one(X2) ) ).

cnf(i_0_4489,axiom,
    ( X1 != X2
    | combs(X1,X3,X4) = combs(X2,X3,X4) ) ).

cnf(i_0_4490,axiom,
    ( X1 != X2
    | combs(X3,X1,X4) = combs(X3,X2,X4) ) ).

cnf(i_0_4491,axiom,
    ( X1 != X2
    | combs(X3,X4,X1) = combs(X3,X4,X2) ) ).

cnf(i_0_4492,axiom,
    ( X1 != X2
    | fequal(X1) = fequal(X2) ) ).

cnf(i_0_4493,axiom,
    ( X1 != X2
    | semilattice_sup_sup(X1) = semilattice_sup_sup(X2) ) ).

cnf(i_0_4494,axiom,
    ( X1 != X2
    | semilattice_inf_inf(X1) = semilattice_inf_inf(X2) ) ).

cnf(i_0_4495,axiom,
    ( X1 != X2
    | ord_less_eq(X1) = ord_less_eq(X2) ) ).

cnf(i_0_4496,axiom,
    ( X1 != X2
    | big_co1399186613setsum(X1,X3) = big_co1399186613setsum(X2,X3) ) ).

cnf(i_0_4497,axiom,
    ( X1 != X2
    | big_co1399186613setsum(X3,X1) = big_co1399186613setsum(X3,X2) ) ).

cnf(i_0_4498,axiom,
    ( X1 != X2
    | collect(X1) = collect(X2) ) ).

cnf(i_0_4499,axiom,
    ( X1 != X2
    | finite_card(X1) = finite_card(X2) ) ).

cnf(i_0_4500,axiom,
    ( X1 != X2
    | combi(X1) = combi(X2) ) ).

cnf(i_0_4501,axiom,
    ( X1 != X2
    | zero_zero(X1) = zero_zero(X2) ) ).

cnf(i_0_4502,axiom,
    ( X1 != X2
    | image(X1,X3) = image(X2,X3) ) ).

cnf(i_0_4503,axiom,
    ( X1 != X2
    | image(X3,X1) = image(X3,X2) ) ).

cnf(i_0_4504,axiom,
    ( X1 != X2
    | finite_finite_1(X1) = finite_finite_1(X2) ) ).

cnf(i_0_4505,axiom,
    ( X1 != X2
    | pi(X1,X3) = pi(X2,X3) ) ).

cnf(i_0_4506,axiom,
    ( X1 != X2
    | pi(X3,X1) = pi(X3,X2) ) ).

cnf(i_0_4507,axiom,
    ( X1 != X2
    | combk(X1,X3) = combk(X2,X3) ) ).

cnf(i_0_4508,axiom,
    ( X1 != X2
    | combk(X3,X1) = combk(X3,X2) ) ).

cnf(i_0_4509,axiom,
    ( X1 != X2
    | member(X1) = member(X2) ) ).

cnf(i_0_4510,axiom,
    ( X1 != X2
    | compose(X1,X3,X4) = compose(X2,X3,X4) ) ).

cnf(i_0_4511,axiom,
    ( X1 != X2
    | compose(X3,X1,X4) = compose(X3,X2,X4) ) ).

cnf(i_0_4512,axiom,
    ( X1 != X2
    | compose(X3,X4,X1) = compose(X3,X4,X2) ) ).

cnf(i_0_4513,axiom,
    ( X1 != X2
    | hilbert_inv_into(X1,X3) = hilbert_inv_into(X2,X3) ) ).

cnf(i_0_4514,axiom,
    ( X1 != X2
    | hilbert_inv_into(X3,X1) = hilbert_inv_into(X3,X2) ) ).

cnf(i_0_4515,axiom,
    ( X1 != X2
    | comp(X1,X3,X4) = comp(X2,X3,X4) ) ).

cnf(i_0_4516,axiom,
    ( X1 != X2
    | comp(X3,X1,X4) = comp(X3,X2,X4) ) ).

cnf(i_0_4517,axiom,
    ( X1 != X2
    | comp(X3,X4,X1) = comp(X3,X4,X2) ) ).

cnf(i_0_4518,axiom,
    ( X1 != X2
    | inj_on(X1,X3) = inj_on(X2,X3) ) ).

cnf(i_0_4519,axiom,
    ( X1 != X2
    | inj_on(X3,X1) = inj_on(X3,X2) ) ).

cnf(i_0_4520,axiom,
    ( X1 != X2
    | the_inv_into(X1,X3) = the_inv_into(X2,X3) ) ).

cnf(i_0_4521,axiom,
    ( X1 != X2
    | the_inv_into(X3,X1) = the_inv_into(X3,X2) ) ).

cnf(i_0_4522,axiom,
    ( X1 != X2
    | restrict(X1,X3) = restrict(X2,X3) ) ).

cnf(i_0_4523,axiom,
    ( X1 != X2
    | restrict(X3,X1) = restrict(X3,X2) ) ).

cnf(i_0_4524,axiom,
    ( X1 != X2
    | finite_folding_image(X1,X3) = finite_folding_image(X2,X3) ) ).

cnf(i_0_4525,axiom,
    ( X1 != X2
    | finite_folding_image(X3,X1) = finite_folding_image(X3,X2) ) ).

cnf(i_0_4526,axiom,
    ( X1 != X2
    | ring_1_Ints(X1) = ring_1_Ints(X2) ) ).

cnf(i_0_4527,axiom,
    ( X1 != X2
    | ord_atLeastAtMost(X1) = ord_atLeastAtMost(X2) ) ).

cnf(i_0_4528,axiom,
    ( X1 != X2
    | finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).

cnf(i_0_4529,axiom,
    ( X1 != X2
    | finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).

cnf(i_0_4530,axiom,
    ( X1 != X2
    | finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).

cnf(i_0_4531,axiom,
    ( X1 != X2
    | finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).

cnf(i_0_4532,axiom,
    ( X1 != X2
    | mlex_prod(X1) = mlex_prod(X2) ) ).

cnf(i_0_4533,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4534,axiom,
    ( X1 != X2
    | ~ linordered_idom(X1)
    | linordered_idom(X2) ) ).

cnf(i_0_4535,axiom,
    ( X1 != X2
    | ~ linord1278240602ring_1(X1)
    | linord1278240602ring_1(X2) ) ).

cnf(i_0_4536,axiom,
    ( X1 != X2
    | ~ linord626643107strict(X1)
    | linord626643107strict(X2) ) ).

cnf(i_0_4537,axiom,
    ( X1 != X2
    | ~ lattice(X1)
    | lattice(X2) ) ).

cnf(i_0_4538,axiom,
    ( X1 != X2
    | ~ semiring(X1)
    | semiring(X2) ) ).

cnf(i_0_4539,axiom,
    ( X1 != X2
    | ~ dense_linorder(X1)
    | dense_linorder(X2) ) ).

cnf(i_0_4540,axiom,
    ( X1 != X2
    | ~ linorder(X1)
    | linorder(X2) ) ).

cnf(i_0_4541,axiom,
    ( X1 != X2
    | ~ linord20386208strict(X1)
    | linord20386208strict(X2) ) ).

cnf(i_0_4542,axiom,
    ( X1 != X2
    | ~ linordered_semiring(X1)
    | linordered_semiring(X2) ) ).

cnf(i_0_4543,axiom,
    ( X1 != X2
    | ~ ordered_semiring(X1)
    | ordered_semiring(X2) ) ).

cnf(i_0_4544,axiom,
    ( X1 != X2
    | ~ comm_monoid_mult(X1)
    | comm_monoid_mult(X2) ) ).

cnf(i_0_4545,axiom,
    ( X1 != X2
    | ~ ordere236663937imp_le(X1)
    | ordere236663937imp_le(X2) ) ).

cnf(i_0_4546,axiom,
    ( X1 != X2
    | ~ semiri456707255roduct(X1)
    | semiri456707255roduct(X2) ) ).

cnf(i_0_4547,axiom,
    ( X1 != X2
    | ~ linord1117847801e_zero(X1)
    | linord1117847801e_zero(X2) ) ).

cnf(i_0_4548,axiom,
    ( X1 != X2
    | ~ ordere1490568538miring(X1)
    | ordere1490568538miring(X2) ) ).

cnf(i_0_4549,axiom,
    ( X1 != X2
    | ~ linord893533164strict(X1)
    | linord893533164strict(X2) ) ).

cnf(i_0_4550,axiom,
    ( X1 != X2
    | ~ ordered_ring(X1)
    | ordered_ring(X2) ) ).

cnf(i_0_4551,axiom,
    ( X1 != X2
    | ~ semilattice_sup(X1)
    | semilattice_sup(X2) ) ).

cnf(i_0_4552,axiom,
    ( X1 != X2
    | ~ semilattice_inf(X1)
    | semilattice_inf(X2) ) ).

cnf(i_0_4553,axiom,
    ( X1 != X2
    | ~ ordere779506340up_add(X1)
    | ordere779506340up_add(X2) ) ).

cnf(i_0_4554,axiom,
    ( X1 != X2
    | ~ ordere223160158up_add(X1)
    | ordere223160158up_add(X2) ) ).

cnf(i_0_4555,axiom,
    ( X1 != X2
    | ~ comm_monoid_add(X1)
    | comm_monoid_add(X2) ) ).

cnf(i_0_4556,axiom,
    ( X1 != X2
    | ~ comm_semiring_1(X1)
    | comm_semiring_1(X2) ) ).

cnf(i_0_4557,axiom,
    ( X1 != X2
    | ~ linord219039673up_add(X1)
    | linord219039673up_add(X2) ) ).

cnf(i_0_4558,axiom,
    ( X1 != X2
    | ~ ring_1(X1)
    | ring_1(X2) ) ).

cnf(i_0_4559,axiom,
    ( X1 != X2
    | ~ ordere453448008miring(X1)
    | ordere453448008miring(X2) ) ).

cnf(i_0_4560,axiom,
    ( X1 != X2
    | ~ ordere216010020id_add(X1)
    | ordere216010020id_add(X2) ) ).

cnf(i_0_4561,axiom,
    ( X1 != X2
    | ~ linordered_semidom(X1)
    | linordered_semidom(X2) ) ).

cnf(i_0_4562,axiom,
    ( X1 != X2
    | ~ linordered_field(X1)
    | linordered_field(X2) ) ).

cnf(i_0_4563,axiom,
    ( X1 != X2
    | ~ distrib_lattice(X1)
    | distrib_lattice(X2) ) ).

cnf(i_0_4564,axiom,
    ( X1 != X2
    | ~ comm_semiring(X1)
    | comm_semiring(X2) ) ).

cnf(i_0_4565,axiom,
    ( X1 != X2
    | ~ ring_char_0(X1)
    | ring_char_0(X2) ) ).

cnf(i_0_4566,axiom,
    ( X1 != X2
    | ~ semiring_0(X1)
    | semiring_0(X2) ) ).

cnf(i_0_4567,axiom,
    ( X1 != X2
    | ~ preorder(X1)
    | preorder(X2) ) ).

cnf(i_0_4568,axiom,
    ( X1 != X2
    | ~ ab_semigroup_add(X1)
    | ab_semigroup_add(X2) ) ).

cnf(i_0_4569,axiom,
    ( X1 != X2
    | ~ ab_sem1668676832m_mult(X1)
    | ab_sem1668676832m_mult(X2) ) ).

cnf(i_0_4570,axiom,
    ( X1 != X2
    | ~ cancel_semigroup_add(X1)
    | cancel_semigroup_add(X2) ) ).

cnf(i_0_4571,axiom,
    ( X1 != X2
    | ~ cancel146912293up_add(X1)
    | cancel146912293up_add(X2) ) ).

cnf(i_0_4572,axiom,
    ( X1 != X2
    | ~ top(X1)
    | top(X2) ) ).

cnf(i_0_4573,axiom,
    ( X1 != X2
    | ~ ring_n68954251visors(X1)
    | ring_n68954251visors(X2) ) ).

cnf(i_0_4574,axiom,
    ( X1 != X2
    | ~ no_zero_divisors(X1)
    | no_zero_divisors(X2) ) ).

cnf(i_0_4575,axiom,
    ( X1 != X2
    | ~ bounded_lattice_top(X1)
    | bounded_lattice_top(X2) ) ).

cnf(i_0_4576,axiom,
    ( X1 != X2
    | ~ monoid_mult(X1)
    | monoid_mult(X2) ) ).

cnf(i_0_4577,axiom,
    ( X1 != X2
    | ~ order(X1)
    | order(X2) ) ).

cnf(i_0_4578,axiom,
    ( X1 != X2
    | ~ monoid_add(X1)
    | monoid_add(X2) ) ).

cnf(i_0_4579,axiom,
    ( X1 != X2
    | ~ mult_zero(X1)
    | mult_zero(X2) ) ).

cnf(i_0_4580,axiom,
    ( X1 != X2
    | ~ finite_finite(X1)
    | finite_finite(X2) ) ).

cnf(i_0_4581,axiom,
    ( X1 != X2
    | ~ zero(X1)
    | zero(X2) ) ).

cnf(i_0_4582,axiom,
    ( X1 != X2
    | ~ one(X1)
    | one(X2) ) ).

cnf(i_0_4583,axiom,
    ( X1 != X2
    | ~ bounded_lattice(X1)
    | bounded_lattice(X2) ) ).

cnf(i_0_4584,axiom,
    ( X1 != X2
    | ~ zero_neq_one(X1)
    | zero_neq_one(X2) ) ).

cnf(i_0_4585,axiom,
    ( X1 != X2
    | ~ ord(X1)
    | ord(X2) ) ).

cnf(i_0_4586,axiom,
    ( X1 != X2
    | ~ linord581940658strict(X1)
    | linord581940658strict(X2) ) ).

cnf(i_0_4587,axiom,
    ( X1 != X2
    | ~ linordered_ring(X1)
    | linordered_ring(X2) ) ).

cnf(i_0_4588,axiom,
    ( X1 != X2
    | ~ ab_semigroup_mult(X1)
    | ab_semigroup_mult(X2) ) ).

cnf(i_0_4447_001,axiom,
    X1 = X1 ).

cnf(i_0_4448_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4449_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4450_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3,X4,X5) = hAPP(X2,X3,X4,X5) ) ).

cnf(i_0_4451_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1,X4,X5) = hAPP(X3,X2,X4,X5) ) ).

cnf(i_0_4452_006,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X1,X5) = hAPP(X3,X4,X2,X5) ) ).

cnf(i_0_4453_007,axiom,
    ( X1 != X2
    | hAPP(X3,X4,X5,X1) = hAPP(X3,X4,X5,X2) ) ).

cnf(i_0_4454_008,axiom,
    ( X1 != X2
    | times_times(X1) = times_times(X2) ) ).

cnf(i_0_4455_009,axiom,
    ( X1 != X2
    | top_top(X1) = top_top(X2) ) ).

cnf(i_0_4456_010,axiom,
    ( X1 != X2
    | extensional(X1,X3) = extensional(X2,X3) ) ).

cnf(i_0_4457_011,axiom,
    ( X1 != X2
    | extensional(X3,X1) = extensional(X3,X2) ) ).

cnf(i_0_4458_012,axiom,
    ( X1 != X2
    | finite_psubset(X1) = finite_psubset(X2) ) ).

cnf(i_0_4459_013,axiom,
    ( X1 != X2
    | ord_atLeastLessThan(X1) = ord_atLeastLessThan(X2) ) ).

cnf(i_0_4460_014,axiom,
    ( X1 != X2
    | ord_gr676655987ssThan(X1) = ord_gr676655987ssThan(X2) ) ).

cnf(i_0_4461_015,axiom,
    ( X1 != X2
    | ord_gr1471790799AtMost(X1) = ord_gr1471790799AtMost(X2) ) ).

cnf(i_0_4462_016,axiom,
    ( X1 != X2
    | measure(X1) = measure(X2) ) ).

cnf(i_0_4463_017,axiom,
    ( X1 != X2
    | in_rel(X1,X3) = in_rel(X2,X3) ) ).

cnf(i_0_4464_018,axiom,
    ( X1 != X2
    | in_rel(X3,X1) = in_rel(X3,X2) ) ).

cnf(i_0_4465_019,axiom,
    ( X1 != X2
    | finite_folding_idem(X1,X3) = finite_folding_idem(X2,X3) ) ).

cnf(i_0_4466_020,axiom,
    ( X1 != X2
    | finite_folding_idem(X3,X1) = finite_folding_idem(X3,X2) ) ).

cnf(i_0_4467_021,axiom,
    ( X1 != X2
    | nat_case(X1) = nat_case(X2) ) ).

cnf(i_0_4468_022,axiom,
    ( X1 != X2
    | sum_Plus(X1,X3) = sum_Plus(X2,X3) ) ).

cnf(i_0_4469_023,axiom,
    ( X1 != X2
    | sum_Plus(X3,X1) = sum_Plus(X3,X2) ) ).

cnf(i_0_4470_024,axiom,
    ( X1 != X2
    | ord_greaterThan(X1) = ord_greaterThan(X2) ) ).

cnf(i_0_4471_025,axiom,
    ( X1 != X2
    | ord_atLeast(X1) = ord_atLeast(X2) ) ).

cnf(i_0_4472_026,axiom,
    ( X1 != X2
    | product_Pair(X1,X3) = product_Pair(X2,X3) ) ).

cnf(i_0_4473_027,axiom,
    ( X1 != X2
    | product_Pair(X3,X1) = product_Pair(X3,X2) ) ).

cnf(i_0_4474_028,axiom,
    ( X1 != X2
    | combc(X1,X3,X4) = combc(X2,X3,X4) ) ).

cnf(i_0_4475_029,axiom,
    ( X1 != X2
    | combc(X3,X1,X4) = combc(X3,X2,X4) ) ).

cnf(i_0_4476_030,axiom,
    ( X1 != X2
    | combc(X3,X4,X1) = combc(X3,X4,X2) ) ).

cnf(i_0_4477_031,axiom,
    ( X1 != X2
    | product_prod_rec(X1,X3,X4) = product_prod_rec(X2,X3,X4) ) ).

cnf(i_0_4478_032,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X1,X4) = product_prod_rec(X3,X2,X4) ) ).

cnf(i_0_4479_033,axiom,
    ( X1 != X2
    | product_prod_rec(X3,X4,X1) = product_prod_rec(X3,X4,X2) ) ).

cnf(i_0_4480_034,axiom,
    ( X1 != X2
    | combb(X1,X3,X4) = combb(X2,X3,X4) ) ).

cnf(i_0_4481_035,axiom,
    ( X1 != X2
    | combb(X3,X1,X4) = combb(X3,X2,X4) ) ).

cnf(i_0_4482_036,axiom,
    ( X1 != X2
    | combb(X3,X4,X1) = combb(X3,X4,X2) ) ).

cnf(i_0_4483_037,axiom,
    ( X1 != X2
    | size_size(X1) = size_size(X2) ) ).

cnf(i_0_4484_038,axiom,
    ( X1 != X2
    | if(X1) = if(X2) ) ).

cnf(i_0_4485_039,axiom,
    ( X1 != X2
    | undefined(X1) = undefined(X2) ) ).

cnf(i_0_4486_040,axiom,
    ( X1 != X2
    | ord_less(X1) = ord_less(X2) ) ).

cnf(i_0_4487_041,axiom,
    ( X1 != X2
    | plus_plus(X1) = plus_plus(X2) ) ).

cnf(i_0_4488_042,axiom,
    ( X1 != X2
    | one_one(X1) = one_one(X2) ) ).

cnf(i_0_4489_043,axiom,
    ( X1 != X2
    | combs(X1,X3,X4) = combs(X2,X3,X4) ) ).

cnf(i_0_4490_044,axiom,
    ( X1 != X2
    | combs(X3,X1,X4) = combs(X3,X2,X4) ) ).

cnf(i_0_4491_045,axiom,
    ( X1 != X2
    | combs(X3,X4,X1) = combs(X3,X4,X2) ) ).

cnf(i_0_4492_046,axiom,
    ( X1 != X2
    | fequal(X1) = fequal(X2) ) ).

cnf(i_0_4493_047,axiom,
    ( X1 != X2
    | semilattice_sup_sup(X1) = semilattice_sup_sup(X2) ) ).

cnf(i_0_4494_048,axiom,
    ( X1 != X2
    | semilattice_inf_inf(X1) = semilattice_inf_inf(X2) ) ).

cnf(i_0_4495_049,axiom,
    ( X1 != X2
    | ord_less_eq(X1) = ord_less_eq(X2) ) ).

cnf(i_0_4496_050,axiom,
    ( X1 != X2
    | big_co1399186613setsum(X1,X3) = big_co1399186613setsum(X2,X3) ) ).

cnf(i_0_4497_051,axiom,
    ( X1 != X2
    | big_co1399186613setsum(X3,X1) = big_co1399186613setsum(X3,X2) ) ).

cnf(i_0_4498_052,axiom,
    ( X1 != X2
    | collect(X1) = collect(X2) ) ).

cnf(i_0_4499_053,axiom,
    ( X1 != X2
    | finite_card(X1) = finite_card(X2) ) ).

cnf(i_0_4500_054,axiom,
    ( X1 != X2
    | combi(X1) = combi(X2) ) ).

cnf(i_0_4501_055,axiom,
    ( X1 != X2
    | zero_zero(X1) = zero_zero(X2) ) ).

cnf(i_0_4502_056,axiom,
    ( X1 != X2
    | image(X1,X3) = image(X2,X3) ) ).

cnf(i_0_4503_057,axiom,
    ( X1 != X2
    | image(X3,X1) = image(X3,X2) ) ).

cnf(i_0_4504_058,axiom,
    ( X1 != X2
    | finite_finite_1(X1) = finite_finite_1(X2) ) ).

cnf(i_0_4505_059,axiom,
    ( X1 != X2
    | pi(X1,X3) = pi(X2,X3) ) ).

cnf(i_0_4506_060,axiom,
    ( X1 != X2
    | pi(X3,X1) = pi(X3,X2) ) ).

cnf(i_0_4507_061,axiom,
    ( X1 != X2
    | combk(X1,X3) = combk(X2,X3) ) ).

cnf(i_0_4508_062,axiom,
    ( X1 != X2
    | combk(X3,X1) = combk(X3,X2) ) ).

cnf(i_0_4509_063,axiom,
    ( X1 != X2
    | member(X1) = member(X2) ) ).

cnf(i_0_4510_064,axiom,
    ( X1 != X2
    | compose(X1,X3,X4) = compose(X2,X3,X4) ) ).

cnf(i_0_4511_065,axiom,
    ( X1 != X2
    | compose(X3,X1,X4) = compose(X3,X2,X4) ) ).

cnf(i_0_4512_066,axiom,
    ( X1 != X2
    | compose(X3,X4,X1) = compose(X3,X4,X2) ) ).

cnf(i_0_4513_067,axiom,
    ( X1 != X2
    | hilbert_inv_into(X1,X3) = hilbert_inv_into(X2,X3) ) ).

cnf(i_0_4514_068,axiom,
    ( X1 != X2
    | hilbert_inv_into(X3,X1) = hilbert_inv_into(X3,X2) ) ).

cnf(i_0_4515_069,axiom,
    ( X1 != X2
    | comp(X1,X3,X4) = comp(X2,X3,X4) ) ).

cnf(i_0_4516_070,axiom,
    ( X1 != X2
    | comp(X3,X1,X4) = comp(X3,X2,X4) ) ).

cnf(i_0_4517_071,axiom,
    ( X1 != X2
    | comp(X3,X4,X1) = comp(X3,X4,X2) ) ).

cnf(i_0_4518_072,axiom,
    ( X1 != X2
    | inj_on(X1,X3) = inj_on(X2,X3) ) ).

cnf(i_0_4519_073,axiom,
    ( X1 != X2
    | inj_on(X3,X1) = inj_on(X3,X2) ) ).

cnf(i_0_4520_074,axiom,
    ( X1 != X2
    | the_inv_into(X1,X3) = the_inv_into(X2,X3) ) ).

cnf(i_0_4521_075,axiom,
    ( X1 != X2
    | the_inv_into(X3,X1) = the_inv_into(X3,X2) ) ).

cnf(i_0_4522_076,axiom,
    ( X1 != X2
    | restrict(X1,X3) = restrict(X2,X3) ) ).

cnf(i_0_4523_077,axiom,
    ( X1 != X2
    | restrict(X3,X1) = restrict(X3,X2) ) ).

cnf(i_0_4524_078,axiom,
    ( X1 != X2
    | finite_folding_image(X1,X3) = finite_folding_image(X2,X3) ) ).

cnf(i_0_4525_079,axiom,
    ( X1 != X2
    | finite_folding_image(X3,X1) = finite_folding_image(X3,X2) ) ).

cnf(i_0_4526_080,axiom,
    ( X1 != X2
    | ring_1_Ints(X1) = ring_1_Ints(X2) ) ).

cnf(i_0_4527_081,axiom,
    ( X1 != X2
    | ord_atLeastAtMost(X1) = ord_atLeastAtMost(X2) ) ).

cnf(i_0_4528_082,axiom,
    ( X1 != X2
    | finite_fold_image(X1,X3) = finite_fold_image(X2,X3) ) ).

cnf(i_0_4529_083,axiom,
    ( X1 != X2
    | finite_fold_image(X3,X1) = finite_fold_image(X3,X2) ) ).

cnf(i_0_4530_084,axiom,
    ( X1 != X2
    | finite908156982e_idem(X1,X3) = finite908156982e_idem(X2,X3) ) ).

cnf(i_0_4531_085,axiom,
    ( X1 != X2
    | finite908156982e_idem(X3,X1) = finite908156982e_idem(X3,X2) ) ).

cnf(i_0_4532_086,axiom,
    ( X1 != X2
    | mlex_prod(X1) = mlex_prod(X2) ) ).

cnf(i_0_4533_087,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4534_088,axiom,
    ( X1 != X2
    | ~ linordered_idom(X1)
    | linordered_idom(X2) ) ).

cnf(i_0_4535_089,axiom,
    ( X1 != X2
    | ~ linord1278240602ring_1(X1)
    | linord1278240602ring_1(X2) ) ).

cnf(i_0_4536_090,axiom,
    ( X1 != X2
    | ~ linord626643107strict(X1)
    | linord626643107strict(X2) ) ).

cnf(i_0_4537_091,axiom,
    ( X1 != X2
    | ~ lattice(X1)
    | lattice(X2) ) ).

cnf(i_0_4538_092,axiom,
    ( X1 != X2
    | ~ semiring(X1)
    | semiring(X2) ) ).

cnf(i_0_4539_093,axiom,
    ( X1 != X2
    | ~ dense_linorder(X1)
    | dense_linorder(X2) ) ).

cnf(i_0_4540_094,axiom,
    ( X1 != X2
    | ~ linorder(X1)
    | linorder(X2) ) ).

cnf(i_0_4541_095,axiom,
    ( X1 != X2
    | ~ linord20386208strict(X1)
    | linord20386208strict(X2) ) ).

cnf(i_0_4542_096,axiom,
    ( X1 != X2
    | ~ linordered_semiring(X1)
    | linordered_semiring(X2) ) ).

cnf(i_0_4543_097,axiom,
    ( X1 != X2
    | ~ ordered_semiring(X1)
    | ordered_semiring(X2) ) ).

cnf(i_0_4544_098,axiom,
    ( X1 != X2
    | ~ comm_monoid_mult(X1)
    | comm_monoid_mult(X2) ) ).

cnf(i_0_4545_099,axiom,
    ( X1 != X2
    | ~ ordere236663937imp_le(X1)
    | ordere236663937imp_le(X2) ) ).

cnf(i_0_4546_100,axiom,
    ( X1 != X2
    | ~ semiri456707255roduct(X1)
    | semiri456707255roduct(X2) ) ).

cnf(i_0_4547_101,axiom,
    ( X1 != X2
    | ~ linord1117847801e_zero(X1)
    | linord1117847801e_zero(X2) ) ).

cnf(i_0_4548_102,axiom,
    ( X1 != X2
    | ~ ordere1490568538miring(X1)
    | ordere1490568538miring(X2) ) ).

cnf(i_0_4549_103,axiom,
    ( X1 != X2
    | ~ linord893533164strict(X1)
    | linord893533164strict(X2) ) ).

cnf(i_0_4550_104,axiom,
    ( X1 != X2
    | ~ ordered_ring(X1)
    | ordered_ring(X2) ) ).

cnf(i_0_4551_105,axiom,
    ( X1 != X2
    | ~ semilattice_sup(X1)
    | semilattice_sup(X2) ) ).

cnf(i_0_4552_106,axiom,
    ( X1 != X2
    | ~ semilattice_inf(X1)
    | semilattice_inf(X2) ) ).

cnf(i_0_4553_107,axiom,
    ( X1 != X2
    | ~ ordere779506340up_add(X1)
    | ordere779506340up_add(X2) ) ).

cnf(i_0_4554_108,axiom,
    ( X1 != X2
    | ~ ordere223160158up_add(X1)
    | ordere223160158up_add(X2) ) ).

cnf(i_0_4555_109,axiom,
    ( X1 != X2
    | ~ comm_monoid_add(X1)
    | comm_monoid_add(X2) ) ).

cnf(i_0_4556_110,axiom,
    ( X1 != X2
    | ~ comm_semiring_1(X1)
    | comm_semiring_1(X2) ) ).

cnf(i_0_4557_111,axiom,
    ( X1 != X2
    | ~ linord219039673up_add(X1)
    | linord219039673up_add(X2) ) ).

cnf(i_0_4558_112,axiom,
    ( X1 != X2
    | ~ ring_1(X1)
    | ring_1(X2) ) ).

cnf(i_0_4559_113,axiom,
    ( X1 != X2
    | ~ ordere453448008miring(X1)
    | ordere453448008miring(X2) ) ).

cnf(i_0_4560_114,axiom,
    ( X1 != X2
    | ~ ordere216010020id_add(X1)
    | ordere216010020id_add(X2) ) ).

cnf(i_0_4561_115,axiom,
    ( X1 != X2
    | ~ linordered_semidom(X1)
    | linordered_semidom(X2) ) ).

cnf(i_0_4562_116,axiom,
    ( X1 != X2
    | ~ linordered_field(X1)
    | linordered_field(X2) ) ).

cnf(i_0_4563_117,axiom,
    ( X1 != X2
    | ~ distrib_lattice(X1)
    | distrib_lattice(X2) ) ).

cnf(i_0_4564_118,axiom,
    ( X1 != X2
    | ~ comm_semiring(X1)
    | comm_semiring(X2) ) ).

cnf(i_0_4565_119,axiom,
    ( X1 != X2
    | ~ ring_char_0(X1)
    | ring_char_0(X2) ) ).

cnf(i_0_4566_120,axiom,
    ( X1 != X2
    | ~ semiring_0(X1)
    | semiring_0(X2) ) ).

cnf(i_0_4567_121,axiom,
    ( X1 != X2
    | ~ preorder(X1)
    | preorder(X2) ) ).

cnf(i_0_4568_122,axiom,
    ( X1 != X2
    | ~ ab_semigroup_add(X1)
    | ab_semigroup_add(X2) ) ).

cnf(i_0_4569_123,axiom,
    ( X1 != X2
    | ~ ab_sem1668676832m_mult(X1)
    | ab_sem1668676832m_mult(X2) ) ).

cnf(i_0_4570_124,axiom,
    ( X1 != X2
    | ~ cancel_semigroup_add(X1)
    | cancel_semigroup_add(X2) ) ).

cnf(i_0_4571_125,axiom,
    ( X1 != X2
    | ~ cancel146912293up_add(X1)
    | cancel146912293up_add(X2) ) ).

cnf(i_0_4572_126,axiom,
    ( X1 != X2
    | ~ top(X1)
    | top(X2) ) ).

cnf(i_0_4573_127,axiom,
    ( X1 != X2
    | ~ ring_n68954251visors(X1)
    | ring_n68954251visors(X2) ) ).

cnf(i_0_4574_128,axiom,
    ( X1 != X2
    | ~ no_zero_divisors(X1)
    | no_zero_divisors(X2) ) ).

cnf(i_0_4575_129,axiom,
    ( X1 != X2
    | ~ bounded_lattice_top(X1)
    | bounded_lattice_top(X2) ) ).

cnf(i_0_4576_130,axiom,
    ( X1 != X2
    | ~ monoid_mult(X1)
    | monoid_mult(X2) ) ).

cnf(i_0_4577_131,axiom,
    ( X1 != X2
    | ~ order(X1)
    | order(X2) ) ).

cnf(i_0_4578_132,axiom,
    ( X1 != X2
    | ~ monoid_add(X1)
    | monoid_add(X2) ) ).

cnf(i_0_4579_133,axiom,
    ( X1 != X2
    | ~ mult_zero(X1)
    | mult_zero(X2) ) ).

cnf(i_0_4580_134,axiom,
    ( X1 != X2
    | ~ finite_finite(X1)
    | finite_finite(X2) ) ).

cnf(i_0_4581_135,axiom,
    ( X1 != X2
    | ~ zero(X1)
    | zero(X2) ) ).

cnf(i_0_4582_136,axiom,
    ( X1 != X2
    | ~ one(X1)
    | one(X2) ) ).

cnf(i_0_4583_137,axiom,
    ( X1 != X2
    | ~ bounded_lattice(X1)
    | bounded_lattice(X2) ) ).

cnf(i_0_4584_138,axiom,
    ( X1 != X2
    | ~ zero_neq_one(X1)
    | zero_neq_one(X2) ) ).

cnf(i_0_4585_139,axiom,
    ( X1 != X2
    | ~ ord(X1)
    | ord(X2) ) ).

cnf(i_0_4586_140,axiom,
    ( X1 != X2
    | ~ linord581940658strict(X1)
    | linord581940658strict(X2) ) ).

cnf(i_0_4587_141,axiom,
    ( X1 != X2
    | ~ linordered_ring(X1)
    | linordered_ring(X2) ) ).

cnf(i_0_4588_142,axiom,
    ( X1 != X2
    | ~ ab_semigroup_mult(X1)
    | ab_semigroup_mult(X2) ) ).

cnf(i_0_4589,plain,
    ( hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5) = hAPP(fun(X1,bool),X2,hAPP(fun(X1,X2),fun(fun(X1,bool),X2),X3,X4),X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X5))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool,hAPP(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool),hAPP(fun(X2,fun(X2,X2)),fun(X2,fun(fun(fun(X1,X2),fun(fun(X1,bool),X2)),bool)),finite_folding_image(X2,X1),X6),X7),X3)) ),
    inference(equality_inference,[],[2782]) ).

cnf(i_0_4590,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X1),X2))) ),
    inference(equality_inference,[],[2898]) ).

cnf(i_0_4591,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X2),X1))) ),
    inference(equality_inference,[],[2899]) ).

cnf(i_0_4592,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X2),X1))) ),
    inference(equality_inference,[],[2900]) ).

cnf(i_0_4593,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X1),X2))) ),
    inference(equality_inference,[],[2901]) ).

cnf(i_0_4594,plain,
    ( ~ ab_semigroup_mult(X1)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X3))
    | hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) = hAPP(fun(X2,bool),X1,hAPP(X1,fun(fun(X2,bool),X1),hAPP(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1)),hAPP(fun(X1,fun(X1,X1)),fun(fun(X2,X1),fun(X1,fun(fun(X2,bool),X1))),finite_fold_image(X1,X2),times_times(X1)),X4),X5),X3) ),
    inference(equality_inference,[],[2917]) ).

cnf(i_0_4595,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X3),X1))) ),
    inference(equality_inference,[],[2920]) ).

cnf(i_0_4596,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X1),X3))) ),
    inference(equality_inference,[],[2921]) ).

cnf(i_0_4597,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X2),X1))) ),
    inference(equality_inference,[],[2928]) ).

cnf(i_0_4598,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X1),X2))) ),
    inference(equality_inference,[],[2929]) ).

cnf(i_0_4599,plain,
    ( 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),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X5),X4)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk147_6(X2,X1,X3,X5,X4,X4)),X4)) ),
    inference(equality_inference,[],[2935]) ).

cnf(i_0_4600,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X3),X1))) ),
    inference(equality_inference,[],[2949]) ).

cnf(i_0_4601,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X1),X2))) ),
    inference(equality_inference,[],[2950]) ).

cnf(i_0_4602,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X1),X2))) ),
    inference(equality_inference,[],[2951]) ).

cnf(i_0_4603,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X2),X1))) ),
    inference(equality_inference,[],[2952]) ).

cnf(i_0_4604,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X3)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X3)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X4),X2),X1))) ),
    inference(equality_inference,[],[2957]) ).

cnf(i_0_4605,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X2)),X4))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X4),arrow_1568854078le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X3),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X4),X1),X2))) ),
    inference(equality_inference,[],[2958]) ).

cnf(i_0_4606,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_1665824030_below,X3),X1),X2))) ),
    inference(equality_inference,[],[2965]) ).

cnf(i_0_4607,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),bool),member(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),X3),arrow_1568854078le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X4),X4)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool))),arrow_357225482_above,X3),X1),X2))) ),
    inference(equality_inference,[],[2966]) ).

cnf(i_0_4608,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,[],[3044]) ).

cnf(i_0_4609,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X1))),
    inference(equality_inference,[],[3091]) ).

cnf(i_0_4610,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X2))),
    inference(equality_inference,[],[3092]) ).

cnf(i_0_4611,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)
    | ~ 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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),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,bool),fun(fun(X1,X2),bool),extensional(X1,X2),X4))) ),
    inference(equality_inference,[],[3110]) ).

cnf(i_0_4612,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4) ),
    inference(equality_inference,[],[3186]) ).

cnf(i_0_4613,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2)
    | hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4) ),
    inference(equality_inference,[],[3187]) ).

cnf(i_0_4614,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X1),X2)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1622070166_mkbot,X3),X1))) ),
    inference(equality_inference,[],[3217]) ).

cnf(i_0_4615,plain,
    ( hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X1) = hAPP(arrow_2142409994le_alt,arrow_2142409994le_alt,combi(arrow_2142409994le_alt),X2)
    | hBOOL(hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool,hAPP(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),fun(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),bool),member(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),hAPP(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),hAPP(arrow_2142409994le_alt,fun(arrow_2142409994le_alt,product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt)),product_Pair(arrow_2142409994le_alt,arrow_2142409994le_alt),X2),X1)),hAPP(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),hAPP(fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool),fun(arrow_2142409994le_alt,fun(product_prod(arrow_2142409994le_alt,arrow_2142409994le_alt),bool)),arrow_1770777252_mktop,X3),X1))) ),
    inference(equality_inference,[],[3218]) ).

cnf(i_0_4616,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),esk104_4(X1,X1,X2,combi(X1)))
    | ~ 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))))
    | ~ 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,[],[3272]) ).

cnf(i_0_4617,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X2),X2))) ),
    inference(equality_inference,[],[3279]) ).

cnf(i_0_4618,plain,
    ( 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),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),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),semilattice_sup_sup(fun(X1,bool)),X4),X4))) ),
    inference(equality_inference,[],[3317]) ).

cnf(i_0_4619,plain,
    ( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),esk105_5(X1,X1,X2,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))))
    | 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,[],[3336]) ).

cnf(i_0_4620,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) ),
    inference(equality_inference,[],[3406]) ).

cnf(i_0_4621,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)) ),
    inference(equality_inference,[],[3407]) ).

cnf(i_0_4622,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
    inference(equality_inference,[],[3408]) ).

cnf(i_0_4623,plain,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)) ),
    inference(equality_inference,[],[3409]) ).

cnf(i_0_4624,plain,
    hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4) = hAPP(fun(X1,bool),fun(X1,X2),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X1,X2)),restrict(X1,X2),X3),X4),
    inference(equality_inference,[],[3454]) ).

cnf(i_0_4625,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,[],[3474]) ).

cnf(i_0_4626,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,[],[3478]) ).

cnf(i_0_4627,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,[],[3484]) ).

cnf(i_0_4628,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,[],[3525]) ).

cnf(i_0_4629,plain,
    ( hAPP(X1,X1,hAPP(fun(X1,X1),fun(X1,X1),hAPP(fun(X1,bool),fun(fun(X1,X1),fun(X1,X1)),the_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,[],[3526]) ).

cnf(i_0_4630,plain,
    ( hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),suc),X1) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ 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),zero_zero(nat)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk176_4(nat,suc,X1,zero_zero(nat))),X1)) ),
    inference(equality_inference,[],[3527]) ).

cnf(i_0_4631,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,[],[3583]) ).

cnf(i_0_4632,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,[],[3584]) ).

cnf(i_0_4633,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,[],[3585]) ).

cnf(i_0_4634,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,[],[3586]) ).

cnf(i_0_4635,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6) = hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),comp(X3,X2,X1),X4),X5),X6),
    inference(equality_inference,[],[3595]) ).

cnf(i_0_4636,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),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,[],[3634]) ).

cnf(i_0_4637,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,[],[3643]) ).

cnf(i_0_4638,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,[],[3660]) ).

cnf(i_0_4639,plain,
    ( 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),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),top_top(fun(X1,bool)))) ),
    inference(equality_inference,[],[3689]) ).

cnf(i_0_4640,plain,
    hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)),
    inference(equality_inference,[],[3761]) ).

cnf(i_0_4641,plain,
    hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)) = hAPP(X1,X2,X3,hAPP(X4,X1,X5,X6)),
    inference(equality_inference,[],[3762]) ).

cnf(i_0_4642,plain,
    X1 = X1,
    inference(equality_inference,[],[3778]) ).

cnf(i_0_4643,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,[],[3784]) ).

cnf(i_0_4644,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
    inference(equality_inference,[],[3818]) ).

cnf(i_0_4645,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,[],[3871]) ).

cnf(i_0_4646,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,[],[3873]) ).

cnf(i_0_4647,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,[],[3882]) ).

cnf(i_0_4648,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,[],[3883]) ).

cnf(i_0_4649,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,[],[3918]) ).

cnf(i_0_4650,plain,
    hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
    inference(equality_inference,[],[3956]) ).

cnf(i_0_4651,plain,
    hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2),
    inference(equality_inference,[],[3958]) ).

cnf(i_0_4652,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(equality_inference,[],[3973]) ).

cnf(i_0_4653,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(equality_inference,[],[3977]) ).

cnf(i_0_4654,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,[],[4003]) ).

cnf(i_0_4655,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,[],[4004]) ).

cnf(i_0_4656,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[4019]) ).

cnf(i_0_4657,plain,
    ( ~ cancel146912293up_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[4020]) ).

cnf(i_0_4658,plain,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[4022]) ).

cnf(i_0_4659,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,[],[4023]) ).

cnf(i_0_4660,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,[],[4046]) ).

cnf(i_0_4661,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[4065]) ).

cnf(i_0_4662,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[4066]) ).

cnf(i_0_4663,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(equality_inference,[],[4074]) ).

cnf(i_0_4664,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(equality_inference,[],[4078]) ).

cnf(i_0_4665,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(equality_inference,[],[4079]) ).

cnf(i_0_4666,plain,
    ( X1 = X1
    | X2 = zero_zero(nat) ),
    inference(equality_inference,[],[4080]) ).

cnf(i_0_4667,plain,
    ( X1 = X1
    | X2 = zero_zero(nat) ),
    inference(equality_inference,[],[4082]) ).

cnf(i_0_4668,plain,
    X1 = X1,
    inference(equality_inference,[],[4085]) ).

cnf(i_0_4669,plain,
    X1 = X1,
    inference(equality_inference,[],[4086]) ).

cnf(i_0_4670,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,[],[4095]) ).

cnf(i_0_4671,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,[],[4096]) ).

cnf(i_0_4672,plain,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
    inference(equality_inference,[],[4099]) ).

cnf(i_0_4673,plain,
    hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X2)),
    inference(equality_inference,[],[4100]) ).

cnf(i_0_4674,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,[],[4104]) ).

cnf(i_0_4675,plain,
    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))) = top_top(fun(X1,bool)),
    inference(equality_inference,[],[4114]) ).

cnf(i_0_4676,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(equality_inference,[],[4126]) ).

cnf(i_0_4677,plain,
    ( ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
    inference(equality_inference,[],[4171]) ).

cnf(i_0_4678,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X2),
    inference(equality_inference,[],[4185]) ).

cnf(i_0_4679,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X2),zero_zero(nat)),
    inference(equality_inference,[],[4186]) ).

cnf(i_0_4680,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(equality_inference,[],[4189]) ).

cnf(i_0_4681,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[4212]) ).

cnf(i_0_4682,plain,
    ( ~ linorder(X1)
    | hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X2) ),
    inference(equality_inference,[],[4213]) ).

cnf(i_0_4683,plain,
    ( ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) = hAPP(X1,fun(X1,bool),ord_greaterThan(X1),X2) ),
    inference(equality_inference,[],[4216]) ).

cnf(i_0_4684,plain,
    ( ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) = hAPP(X1,fun(X1,bool),ord_atLeast(X1),X2) ),
    inference(equality_inference,[],[4217]) ).

cnf(i_0_4685,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),X1) = zero_zero(nat),
    inference(equality_inference,[],[4294]) ).

cnf(i_0_4686,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X1),zero_zero(nat)) = zero_zero(nat),
    inference(equality_inference,[],[4295]) ).

cnf(i_0_4687,plain,
    X1 = X1,
    inference(equality_inference,[],[4304]) ).

cnf(i_0_4688,plain,
    $false,
    inference(scs_inference,[],[i_0_3194,i_0_2758,i_0_2750]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SCT171+7 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32  % Computer : n031.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Tue May  5 02:03:38 EDT 2026
% 0.14/0.32  % CPUTime    : 
% 0.14/0.33  % start to proof: theBenchmark
% 2.74/2.94  % Version  : CSE_E---1.7
% 2.74/2.94  % Problem  : theBenchmark.p
% 2.74/2.94  % SZS status Theorem for theBenchmark.p
% 2.74/2.94  % SZS output start CNFRefutation
% See solution above
% 2.86/3.10  % Total time : 2.604s
%------------------------------------------------------------------------------